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# Math OER Turn In Problems

The greatest reward for a student is not a good grade. It is the willingness of his teacher to listen to him.

- Nikolay Konstantinov

These problems are the icing on the cake. They have no answer key. You turn them in to demonstrate you have mastered the topic.

Do this work on scratch paper and get answers you are happy with before you use the website to turn in the homework.

If you score 80% or more you are done with that homework assignment. If you score less, you will need to try again.

As with all other homework, please use the homework to notice where your notes need improvement, and work in study groups when you can.

1. What number is two hundred twelve thousandths?

2. Which is the largest decimal? 0.243, 0.423, 0.324, 0.0423, 0.4023

3. Which is the smallest decimal? 0.243, 0.423, 0.324, 0.0423, 0.4023

4. Round 17,398.967 to the nearest ten.

5. Round 98,807.728 to the nearest tenth.

6. Round 54,498.66118 to the nearest thousand.

7. 2 ÷ 11 = 0.181818... Round that decimal to the nearest thousandth.

8. Alicia's rectangular garden bed has two long sides of length 2.74 meters and two short sides of length 1.22 meters. Estimate the sum of all four sides.

9. Ben's rectangular garden bed has two long sides of length 3.048 meters and two short sides of length 0.9144 meters. Estimate the sum of all four sides.

10. Which garden bed estimate will be closer to the actual sum? How can you know without calculating the actual sums?

After you are very happy with your answers, turn in these Rounding problems here.

1. Consider the following six numbers: 315, 1101, 7628, 13025, 110124, and 876. Which are divisible by 3?

2. Consider the following six numbers: 315, 1101, 7628, 13025, 110124, and 876. Which are divisible by 4?

3. How many factors does 126 have?

4. What is the prime factorization of 126?

5. Fully reduce the fraction 16120

6. Change 0.45 to a fraction. Remember to simplify.

7. What is the decimal notation for four-twentieths?

8. The Leaning Tower of Pisa is 184.5 feet tall and leans 13 feet from its base. What is the ratio of the distance it leans to its height?.

9. The area is 0.75 square miles. The population is 35,427 people. What is the unit rate of people per square mile?

10. Brand M soup weighs 54 ounces and costs \$4.79. Brand T soup weighs 59 ounces and costs \$5.99. Which is the better buy?

After you are very happy with your answers, turn in these Fraction Format problems here.

1. An easy way to divide a number by 1,000 is to scoot the decimal point ___ places to the _____.

2. An easy way to multiply a number by 0.01 is to scoot the decimal point ___ places to the _____.

3. Write 5.5% as a decimal.

4. Write 0.8911 as a percent.

5.Write 0.8% as a fraction.

6. Write 25 38 % as a fraction.

7. Write the fraction 58 as a percent.

8. Write the fraction 1750 as a percent.

9. After we change two-thirds into percent format, do its digits repeat endlessly?

10. Use what you have memorized to write 33 13 percent as a fraction.

After you are very happy with your answers, turn in these Percent Format problems here.

1. 1 foot is how many yards?

2. 7.1 miles is how many feet?

3. 5,280 yards is how many miles?

4. An index card is 0.27 mm thick. What is that thickness in centimeters?

5. An index card is 0.27 mm thick. What is that thickness in meters?

6. A football field is 4,844 cm wide. What is that width in kilometers?

7. 80 ounces is how many pounds?

8.5,200 grams is how many kilograms?

9. One gallon is how many fluid ounces?

10. 806 liters is how many milliliters?

After you are very happy with your answers, turn in these Measurement problems here.

1. A cookie recipe calls for 23 cup of flour. If you are making a double batch, how much flour will you use?

2. What is four-fifths times twenty?

3. What is four-fifths times two-thirds?

4. What is two-thirds divided by three-halves?

5. 2215 ÷ 335 =

6. What is the least common multiple of 12 and 18?

7. What is five-sixths plus three-fourths?

8. What is five-sixths minus three-fourths?

9. A piece of fabric that is 1 34 yards long is cut into seven equal pieces. How long is each piece?

10. Grandma Jorgensen left 23 of her 78 pound silver bullion bar to her son Lloyd. Lloyd gave each of his four children a 14 share. How much silver did each of Lloyd's children receive?

After you are very happy with your answers, turn in these Fractions problems here.

1. What is 25% of 228?

2. What is 40% of 750?

3. The price tag (before sales tax) on an item says \$100. The sales tax rate is 5%. What is the total price (including tax)?

4. During a sale, a dress decreased in price from \$90 to \$72. What was the percent of decrease?

5. An investment increases in value from \$200 to \$216. What is the percent increase?

6. A pinball machine that normall sells for \$3,999 is on sale for \$3,150. What is the rate of discount?

7. Bluebeard has a balance of \$1,834.90 on a credit card with an annual percentage rate of 22.4%. This month's minimum payment is \$36.70. How much less than this minimum payment is the interest? (In other words, if he only pays the minimum payment, how much goes "past" the interest to pay off his principal?)

8. Find the simple interest for a 2 year loan of \$8,000 at a simple interest rate of 12%.

9. Find the simple interest for a 2 month loan of \$8,000 at a simple interest rate of 9.42%.

10. A store takes out a ninety day loan for \$6,500 at 5.25% simple interest. What is the total amount due after ninety days?

After you are very happy with your answers, turn in these Percentages problems here.

1. Two years is how many minutes?

2. A football field is 4,844 cm wide. What is that width in yards? (1 meter ≈ 1.09361 yards)

3. A plane flying 6,500 feet per minute is going about how many miles per hour?

4. Including the end zones, a football field is 360 feet long and 160 feet wide. If you run three laps around a football field, about what percentage of a mile do you run?

5. You want to buy Sculpey III modeling clay online. At amazon.com it costs \$7.29 for 8 ounces. At amazon.co.uk it costs £2.20 for 57 grams. (1 ounce ≈ 28.35 grams. If £1 ≈ \$1.31), which is a better buy?

6. A triangle has base 4 m and height 3.5 m. What is the area?

7. Most billiard tables are twice as long as they are wide. What is the perimeter of a billiard table that measures 4.5 feet by 9 feet?

8. A parallelogram has base 2.3 cm and height 3.5 cm. What is the area?

9. A trapezoid has base 25 cm, top 16 cm, and height 35 cm. What is the area?

10.The standard backyard trampoline has a diameter of 14 feet. What is its area?

After you are very happy with your answers, turn in these Measurement problems here.

1. Is the ratio "2.4 to 3.6" proportional to the ratio "1.8 to 2.7"?

2. Solve the proportion: "7 to 1/4" is proportional to "28 to what?"

3. Fifteen hours of studying before a test lets you score 75 points. At that rate, how many points would you expect from studying 18 hours?

4. Julia's car can drive 120 miles on 4.5 gallons of gas. While driving across the country the tank gets down to 0.9 gallons. How many miles are left, for her to find a gas station?

5. Typically 5 people produce 13 kilograms of garbage each day. How many kilograms of garbage are produced each day by the 346,560 people in Lane County?

6. In a class of 40 students, on average six will be left-handed. A certain class has nine left-handed students. How large would you estimate the class is if its proportion of left-handed students is average?

7. A certain dog medicine contains 3/7 of a gram of active ingredient in every 120 gram dose. For a small dog, how much active ingredient is in a 7 gram dose?

8. A 25 pound turkey serves 18 people. How many pounds does each serving weigh?

9. A 25 pound turkey serves 18 people. What is the unit rate of servings per pound?

10. To determine the number of deer in a game preserve, a forest ranger catches, tags, and releases 318 deer. Later he catches 168 deer and sees that 56 of them are tagged. Use a proportion to estimate the number of deer in the game preserve.

After you are very happy with your answers, turn in these Fractions problems here.

1. What percent of 160 is 150?

2. \$39 is what percent of \$50?

3. 56.32 is 64% of what?

4. 80% of what is 16?

5. 42 is 30% of what number?

6. What number is 150% of 3045?

7. A student got 35 problems correct on a test with 45 problems. What is his percentage score?

8. A salesman earns a 40% commission. One week he earns \$552 in commission. How much did he sell?

9. In my city 85% of the people who take a driver's licence test pass the first time. In January 289 people passed the test. How many people took the test?

10. At the zoo an elephant is put on a diet until it weights only 91% of its original 9,671 pounds. What weight was the diet's goal?

After you are very happy with your answers, turn in these Percentages problems here.

1. 86 degrees Celsius is what temperature in degrees Fahrenheit?

2. 44 degrees Fahrenheit is what temperature in degrees Celsius?

3. A square with sides 10 feet long has the top quarter removed (like a triangular "bite" taken out of the top). What is the remaining area?

4. A circle of radius 6 cm has its southwest quarter removed. What is the perimeter of that "Pac-Man" shape?

5. A half-circle window has diameter of 8 feet. What is its perimeter?

6. You want to install a two foot wide sidewalk around a circular swimming pool. The diameter of the pool is 30 feet. What is the area of the donut-shaped sidewalk, rounded to the nearest square foot?

7. Clarabelle's Confusing Pizza Parlor sells a 20 inch diameter pizza for \$18.99, and a 40 cm diameter pizza for \$14.99. Which is the better buy? (1 inch = 2.54 centimeters.)

8. How large a circle (how big an area?) can fit inside a rectangle of base of 12 feet and height of 5 feet?

9. A square is cut in half. The perimeter of the resulting rectangle is 30 feet. What was the area of the original square?

10. The circumference of a quarter is 7.85 cm. What is its area?

After you are very happy with your answers, turn in these Measurement problems here.

1. Triangular tables are placed in a row to seat more people. One table has 3 seats. Two tables have 4 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

2. Now we switch to square tables. We still make a row of tables to seat more people. One table has 4 seats. Two tables have 6 seats. Create a formula where we put in the number of tables (as n) and get out the number of seats (as y).

3. This shape is sort of like a V or W that gets wider with more wiggles. What is the pattern for how many squares are in each row? (As an optional, extra challenge you can also find the pattern for how many toothpicks are in each row!)

4. How about this extra-wide plus shape? What is the pattern for how many squares are in each row?

5. How about this hollow diamond shape? What is the pattern for how many squares are in each row?

6. This shape looks somewhat like the stand that holds up a road construction sign. With each step it gets longer in each direction. What is the pattern for how many cubes are in each row?

7. There are many versions of an old story about the inventor of the game of chess. One version appears below. On which day will the total grains of rice exceed 3 million?

The Chessboard Story

King Radha of India was bored of backgammon, and desired a new game. Sessa, his minister invented chess. King Radha was pleased and asked Sessa what he desired in payment.

Sessa asked that a single grain of rice be placed on the first square of the chessboard, two grains on the second square, four grains on the third, and so on, doubling each time.

King Radha saw that this would require far more rice than his kingdom would ever produce, and had Sessa executed for impudence.

8. Two trains are approaching each other on parallel tracks. Both are traveling at 30 miles per hour. What is the overall speed at which they approach?

9. Continuing the previous problem, the two trains start 9 miles apart. How many minutes does it take for them to pass each other?

10. Continuing the previous problem, a fly zooms back and forth from the headlight of one train to headlight of the other. It starts when the trains are 9 miles apart. By the time it arrives at the other train, the two trains have gotten closer. It instantly reverses direction and heads back to the first train. And so on. The fly moves at 20 miles per hour. How far does it travel before the trains pass?

The Trains and Fly Story

One day at Los Alamos, Richard Feynman noticed something interesting. When he asked a physicist to solve the Trains and Fly problem they all used the shortcut (as above) and got the answer immediately. When he asked a mathematician, they all calculated the fly's trip bit by bit and finding the answer took several minutes.

Eventually Feynman brought the Trains and Fly problem to the most astounding mathematician of the group, John von Neumann, who immediately answered.

"That's not right!" protested Feynman. "You're a mathematician. You're supposed to sum the series, not use the shortcut!"

"What shortcut?" asked von Neumann. "I did sum the series."

After you are very happy with your answers, turn in these Patterns problems here.

1. Liam weighs 165 pounds. If he swims for 45 minutes, how many calories does he burn?

2. One serving of oatmeal has 3 grams of fat, 31 grams of carbohydrates (including 1 gram from sugar), and 6 grams of protein. Change to calories these amounts of fat, carbohydrate, sugar, and protein.

3. Caroline is an 80 year old woman, not physically active, who weighs 120 pounds and is 5' 3" tall. She walks for 15 minutes to the grocery store, shops for 20 minutes, and walks 15 minutes home. How many calories does she burn?

4. When Caroline walks, 60% of the calories she burns are fat calories (because of her age and other factors). How many fat calories did she burn from her 30 minutes of walking to and from the grocery store?

5. One 1-cup serving of 2% lowfat milk has 5 grams of fat, 12 grams of carbohydrates (all 12 from sugar), and 9 grams of protein. Throughout the day Caroline drinks three cups of 2% milk. How many calories of fat is this?

6. Caroline's DCI is 90% of the USDA expectation of 2,000 calories per day. So her recommended daily fat intake is 65 grams for a 2,000 calorie diet × 0.9 ≈ 59 grams of fat per day. What percentage of her recommended daily fat intake are those three cups of lowfat milk?

7. Zachary is a 35 year old man, moderately active, who weighs 150 pounds and is 5' 7" tall. He bikes for 15 minutes to the gym, lifts weights for 30 minutes, and then bikes 15 minutes home. How many calories does he burn?

8. One 38-gram serving of dark chocolate has 15 grams of fat, 19 grams of carbohydrates (10 from sugar), and 3 grams of protein. Throughout the day Zachary eats four servings of dark chocolate. How many calories of sugar is this?

9. Zachary's DCI is very close to the USDA variation of 2,500 calories per day. He can simply use its recommendation of no more than 63 grams sugar per day. What percentage of his recommended daily sugar intake are those four servings of dark chocolate?

10. Write a formula that outputs the total calories in a food, if you plug in the grams of fat, carbohydrate, and protein.

After you are very happy with your answers, turn in these Calories problems here.

1. Caroline is an 80 year old woman, not physically active, who weighs 120 pounds and is 5' 3" tall. What is Caroline's maximum safe heart rate, minimum aerobic exercise heart rate, and maximum aerobic exercise heart rate?

2. Zachary is a 35 year old man, moderately active, who weighs 150 pounds and is 5' 7" tall. What is Zachary's maximum safe heart rate, minimum aerobic exercise heart rate, and maximum aerobic exercise heart rate?

3. Caroline and Zachary meet at the local Renaissance Fair, as they do every year, for their archery competition. They are nearly silent, and few other fair participants notice the intensity of their rivalry. They shoot for twenty minutes. Archery burns 0.03 calories per pound per minute. How many calories total are burned during this epic struggle?

4. For that archery competition, write Caroline's calories burned as a percentage of Zachary's calories burned.

5. For that archery competition, write Zachary's calories burned as a percentage of Caroline's calories burned.

6. What is Caroline's BMR and DCI?

7. What is Zachary's BMR and DCI?

8. Write Caroline's DCI as a percentage of Zachary's DCI.

9. Caroline has a best friend named Greta, who is also an 80 year old woman, also not physically active, also 5' 3" tall, and who weighs 105 pounds. Find Greta's DCI.

10. Write Greta's DCI as a percentage of Caroline's DCI.

After you are very happy with your answers, turn in these Metabolism problems here.

1. A recipe that makes 8 servings requires 1.5 pounds of trimmed scallions. How many pounds of trimmed scallions will you need if you are scaling up the recipe to make 30 servings?

2. One gallon of whole milk weighs 8.6 pounds. What is the weight of 6.5 cups of whole milk?

3. One cup of uncooked long-grain brown rice weighs 7.2 ounces. What is the weight (in pounds) of one gallon of uncooked long-grain rice?

4. Express 2.88 cups as 2 cups and some tablespoons.

5. Express 6.15 cups as 6 cups and some teaspoons.

6. After scaling up a recipe you get 19 teaspoons of cinnamon. Express this amount in tablespoons and teaspoons.

7. You purchase 20 pounds of celery. How much trimmed celery can you expect this to make?

8. Imagine that you are preparing a large meal for a non-profit fundraiser. Your task is to make the provided meal for 60 people. Find how much of each ingredient you need to purchase, keeping in mind the yield percent for produce. When using eggs you will need to round fractional amounts to the nearest whole number. (Note: spices and directions are omitted for the sake of simplicity.)

9. Use this list of prices to find the total price for the recipes after scaling all three recipes to 60 servings. (Water is considered free.)

 brown rice: \$0.76 per pound carrots: \$0.55 per pound cauliflower: \$1.01 per pound heavy cream: \$2.87 per quart dry milk: \$4.30 per pound honey: \$3.31 per pound large eggs: \$2.75 per dozen milk: \$2.65 per gallon onions: \$0.22 per pound spinach: \$2.35 per pound vegetable broth: \$2.28 per quart whole wheat flour: \$0.57 per pound

10. An elementary school fundraiser includes serving ice cream. The school has a very good idea how much ice cream is needed because it has hosted this event for many years There will be 300 guests attending. 60% of the guests will want a half-cup serving, and the remaining 40% will want one cup of ice cream. As for flavors, 50% of the servings will be vanilla, 30% will be chocolate, and 20% will be strawberry. How many gallons of each flavor ice cream will need to be bought?

After you are very happy with your answers, turn in these Food Preparation problems here.

1. Find the mean of these six numbers: 135, 95, 11, 5, 33, 15.

2. Continuing the previous probem, find the median of those six numbers.

3. The histogram below (original source) shows the number of books read by different children. What is the mean number of books read?

4. Continuing the previous problem, what is the median number of books read?

5. The home values on a certain street, in thousands of dollars, are: 384, 364, 342, 346, 360, 356, 265, 417, and 530. What is the mean of these home values?

6. Continuing the previous problem, what is the median of those home values? Why does this type of average better communicate the "typical" value of a home on that street?

7. A shipping company needs to transport seven freight containers. Their weights are 10, 16, 16, 18, 20, 60, and 77 tons. What is the mean and median weight of these freight containers?

8. Two company clerks receive a report that only contains the mean and median weights, and number of containers, from the previous problem. The first clerk tries to find the total weight by multiplying the mean by the number of containers. The second clerk tries to find the total weight by multiplying the median by the number of containers. Which clerk is correct? Why? How much error does the other clerk have?

9. Some news articles make a big deal when many countries have an average temperate increase well above global average (Alaska, Canada, Russia, Norway, Finland, Switzerland, China, Singapore, Australia, South Africa, etc.) How does a better understanding of averages explain that having many items above average is neither surprising nor sensationalism?

10. During the 2007 strike of the Writer's Guild of America, two different news reports painted very different pictures of these screen and television writers.

• According to CNBC, there were 4,434 guild writers who worked full-time in 2006, and their average salary was \$204,000. (CNBC headline, October 11, 2007)

• According to the Los Angeles Times, the median income of the writers from their guild-covered employment is \$5,000 a year. (Howard A. Rodman, October 17, 2007)

Were Hollywood's writers very wealthy and going to strike even though they earned much more than most Americans? Or were they poor and going on strike to defend the few thousand dollars they could earn from their writing? The headlines leave out two important facts. First, almost half of the guild's writers don't write anything in a given year (their salary that year is \$0). Second, a very few writers earn millions of dollars. How does a better understanding of averages explain the situation more clearly?

After you are very happy with your answers, turn in these Typicality problems here.

The most interesting part of bell curves is how they are used to sort people and shape society. That is not a great source of small math problems! So please pardon a brief tangent into our local contributions towards climate change.

In Oregon, a household's energy usage per month forms a histogram that resembles a bell curve reasonably well for real-life data.

The histogram below shows the monthly electrical useage for a household that has electric heat.

1. In which month does this household use the most electricity?

2. Which month has the least deviation from year to year?

3. Someone asks, "What is this household's typical monthly electrical usage?" What would make a numeric answer to this question meaningful?

4. When did this family replace their old electric furnace with a modern and more efficient heat pump?

5. The total electrical usage for 2017 was 14,780 kilowatt hours. The total electrical usage for 2019 was 11,513 kilowatt hours. How much less electricity was used in 2019?

6. Electricity costs an average of 11.3 cents per kilowatt hour. How much less money was spent on electricity in 2019 than in 2017?

7. What was the percentage decrease of this household's total annual electricity usage when comparing 2017 to 2019?

8. In this city 80% percent of the electric power is from carbon-free hydroelectric energy, making an overall CO2 emission of 16.2 grams per kilowatt hour. How many kilograms of CO2 did this household's electric use create in 2019?

9. A typical gasoline automobile's emission is 8.8 kilograms of CO2 per gallon. This household's car gets 30 miles per gallon. How many miles would they need to drive to the equal CO2 emissions of their annual electricity use?

10. That household actually drives 10,000 miles per year, which is equivalent to about 333 gallons of gasoline. Find this household's total kg of CO2 emissions for house and car, and then divide by 1,000 to convert kilograms to metric tons. Purchasing a carbon offset costs about \$14 per metric ton of CO2. What is the value of the carbon offset cost for this household's house and car?

For most households the energy used to grow and transport food is a larger carbon footprint than home heating or vehicle driving. You can use a website such as CarbonFootprint to estimate your own numbers.

The Central Lane Metropolitan Planning Organization has found that in the Eugene-Springfield area the mean household carbon footprint is 31.9 metric tons of CO2, and the mean carbon footprint per person is 13.8 metric tons of CO2.

After you are very happy with your answers, turn in these Bell Curves problems here.

1. Brenda can afford to spend \$900 per month on mortgage payments, with a 30-year loan. Currently mortgage rates are 5% per year. What price home can she afford?

2. Brenda gets a loan with a 25% downpayment. What will be the size of Brenda's actual mortgage and monthly payment?

3. Brenda's loan has a 2% mortgage fee, first month pre-paid, and \$1,000 other up-front costs. What is the total of her downpayment and these other up-front costs?

4. Zane has an annual income of \$65,000. He wants to spend 30% of his income on a mortgage, with a 15-year loan. The interest rate is 5%. What price home can he afford?

5. Zane gets a loan with a 15% downpayment. What will be the size of Zane's actual mortgage and monthly payment?

6. Zane's loan has a 4% mortgage fee, first month pre-paid, and \$1,300 other up-front costs. What is the total of of his downpayment and these up-front costs?

Remember the Wahl family? Their numbers were:

• budgeted \$1,100 per month on a mortgage
• used a 6% interest rate for a 30 year loan
• wanted a home priced at \$183,000
• used a 20% downpayment, 3% mortgage fee, first month paid up-front, and \$1,100 other up-front costs
• got a \$146,400 mortage with a \$878.40 monthly payment
• over thirty years paid \$314,784, of which \$168,384 was interest

7. Does doubling the monthly payment double the size of the other numbers? Consider the Moneybag family that has initially budgets \$2,200 per month on a mortgage, with everything else the same as the Wahl family. Do the other numbers (except for the fixed "other up-front costs") double?

8. Does halving the length of time halve the size of the other numbers? Consider the Short family that uses a 15 year loan for their mortgage, with everything else the same as the Wahl family. Do the other numbers (except for the fixed "other up-front costs") halve?

9. Does halving the interest rate halve the size of the other numbers? Consider the Timing family that uses a 3% interest for their mortgage, with everything else the same as the Wahl family. (Their Amortization Table value is \$4.22.) Do the other numbers (except for the fixed "other up-front costs") halve?

10. Does doubling the interest rate double the size of the other numbers? Consider the Calamity family that uses a 12% interest for their mortgage, with everything else the same as the Wahl family. (Their Amortization Table value is \$10.29.) Do the other numbers (except for the fixed "other up-front costs") double?

After you are very happy with your answers, turn in these Mortgages problems here.

1. Tom buys a painting for \$100. His friend, Eric, buys a painting for \$200. Both paintings increasse in value by \$30. What is the percent increase for each? How can the two items have different percent appreciation if they both increased by \$30?

2. A business buys a copy machine for \$2,500 by borrowing that \$2,500 with a loan of 15% simple interest for three years and three months. What is the total cost (the copy machine plus the loan's interest)?

3. Oregon Senate Bill 1105 limits payday loan interest rates to 36% or less. Before that bill was passed, payday loans in Oregon often had interest rates of 120%. Nationally, payday loans can have interest rates as high as 7,000%. How much was borrowed at 120% annual simple interest for two weeks if the interest was \$16.15?

(Note: Here is an article describing how check-cashing businesses can be helpful for their community. Nationally, the average payday loan is a two-week advance on \$350.)

4. When Huey, Dewey, and Louie entered kindergarten their uncled started a college account for them. Each account had \$5,000. That one deposit grew at 9% annual interest for 13 years. For Huey the interest was compounded weekly. For Dewey the interest was compounded monthly. For Louie the interest was compounded annually. How much was each account worth at the end of the 13 years?

5. Mr. Largo gives his 20-year-old sibling a \$100 wedding present. The sibling invests it at 11% annual compound interest for 30 years. Then the sibling adds an extra \$10,000, and moves the combined funds in a different investment that earns 4% annual compound interest for 10 years. What is the final value, when the sibling is 60 years old?

6. A credit card has an 18% annual interest rate. Payouts happen monthly. The loan uses compound interest. What is the annual effective interest rate?

7. If \$3,865 is invested with 9% annual compound interest for 40 years, how much will it grow to be worth? How much less than \$176,696 is your answer? These questions are interesting because research by Vanguard shows that the average 25-year-old American has saved \$3,865 for retirement, and the average 65-year-old American has saved \$176,696. We are examining how much more the average American saves beyond the nest egg they have at age 25.

8. Fiddle around using the sum of annuity due formula to find what annual deposit (principal) would grow to \$176,696 over 40 years at 9% annual interest. (Hint: an annual deposit of \$400 is too small, but \$550 is too big.)

The two previous problems show us that it is easy to save as much as an average American. Setting aside less than \$500 per year is enough to be average. Do not be embarassed if you start small with retirement savings. About half of Americans have a below average nest egg at age 25. You can become above average by saving more later in life as your career progresses.

9. How does the long-term financial cost of infant care compare to saving for kids' college expenses? The "big three" child care centers in Eugene cost roughly \$13,000 per year. (Vivian Olum at UO, Early Learning Childrens Community at LCC, and Child Development Center at EWEB. Oregon is an unusually expensive state for child care.) Use the sum of annuity due formula for two years (when the infant is age 1 and 2), and then the compound interest formula for sixteen years (until the child is 18). If the family instead saved the infant care money and earned a 5% annual interest rate, how much would be saved towards the child's college tuition?

10. In a certain computer game the archer queen gets 10% stronger every time she gains a level. Two brothers play the game. The younger brother has a level 20 archer queen. The older brother has a level 27 archer queen. Roughly how much stronger is the older brother's archer queen?

After you are very happy with your answers, turn in these Saving for Retirement problems here.

1. Gavin's tool emporium uses a 40% margin rate. Its most popular item has a \$240 selling price. What is the margin amount?

2. Grace works at a store that uses a 40% markup rate. She orders an item for \$90 wholesale cost. What is the markup amount?

3. Georgina's Vitamin Shop uses a 75% margin rate. It needs to stock a certain bottle of vitamins with a selling price of no more than \$3.50. How much can the shop allow a supplier to charge for this bottle of vitamins?

4. Geoffrey works at a store that uses a 30% markup rate. The wholesale cost of an certain item is at minimum \$22. The store's competitors sell an equivalent item for \$30. Will Geoffrey's store undercut the competition if they stock this item?

5. Galina has a clock that cost her \$62.50. She wants to sell it online for \$102.50, for a profit of \$40. What is the margin rate? What is the markup rate?

6. Grafton works at a sporting goods store, and knows that a certain kind of skis will only sell if it is priced \$109.95 or less. The wholesale cost is \$80. What is the markup rate?

7. A fancy new infant car seat has a skim price of \$220 initially, but the sale price eventually settles at the penetration price of \$150. The wholesale cost is \$67. Divide the larger margin by the smaller margin to find the percentage of extra margin from skimming.

8. A restaurant meal that serves six has \$50 food cost, \$70 labor cost, and \$25 other cost. Find the price per plate using to the desired profit method with a 10% desired profit, and then with the food cost percentage method with a 30% scale factor.

9. The manager of a furniture store knows that a certain table will only sell if the sale price \$250 or less. Currently the sale price is \$275. What percent discount is needed?

10. Giselle works at a candy store. She knows from past years' experience that after Valentine's Day she needs to reduce the prices of the special \$30 chocolate boxes down to \$18 to clear out that inventory. She uses a store-wide sale of 10%, hoping that will attract customers. She also distributes a coupon that further discounts the sale price of just those expensive chocolate boxes. What percent discount is needed on the coupon?

After you are very happy with your answers, turn in these Margin, Markup, and Pricing problems here.

1 to 7. Raynor starts a new credit card that charges 24% annual interest per year to keep his bookkeeping simple when buying a \$1,499 computer. (He will use the card for nothing else.) The credit card charges him one-twelfth of its annual interest rate each month. Raynor pays \$140 per month until the balance is paid off. Fill in the last parts of the table below.

MonthStartingPaymentInterest Due OnInterestEnding
1\$1,499.00\$140\$1,359.00\$27.18\$1,386.18
2\$1,386.18\$140\$1,246.18\$24.92\$1,271.10
3\$1,271.10\$140\$1,131.10\$22.62\$1,153.72
4\$1,153.72\$140\$1,013.72\$20.27\$1,033.99
5\$1,033.99\$140\$893.99\$17.88\$911.87
6\$911.87\$140\$771.87\$15.44\$787.31
7\$787.31\$140\$647.31\$12.95\$660.26
8\$660.26\$140\$520.26\$10.41\$530.67
9\$530.67\$140\$390.67\$7.81#1
10#1\$140#2#3#4
11#4\$140#5#6#7
12#7#7\$0nonepaid off!

8. Continuing the previous problem, find his total interest in dollars.

9. Continuing the previous problem, find what percentage of his first month's payment was interest.

10. Continuing the previous problem, find what percentage of his tenth month's payment was interest.

After you are very happy with your answers, turn in these Charge Options problems here.

1. When rolling two dice, what is the probability of the sum being an even number?

2. When rolling two dice, whatare the odds of the sum being an even number?

3. When rolling two dice, what is the probability of the sum being 8 or more?

4. When rolling two dice, what are the odds of the sum being 8 or more?

5. The medicine trastuzumab, which fights breast cancer in women who already have breast cancer, was popularized because of a certain study. In the control group of 1,700 women, 34 died. In the group treated with trastuzumab, 23 of 1,643 women died. What percentage of the women in the control group died? What percentage of the women in the treated group died?

6. Continuing the previous problem, what was the absolute change (subtraction) in risk?

7. Continuing the previous problem, what was the relative change (percent change) in risk?

8. Trastuzumab also has some dangerous side effects. Most notably, 40% of the women who take it develop flu-like symptoms, 7% develop mild heart problems, and 5% suffer a stroke or severe heart failure. About how many of the 1,643 women in the study who were treated with trastuzumab suffered a stroke or severe heart failure because of drug?

(Tangentially, if you were in charge of publicity for this drug, what type of claim could you truthfully make about the medicine? If you were trying to discredit trastuzumab—perhaps concerned about the side effects and trying to convince a family member with breast cancer not to take the medicine—what type of claim could you truthfully make about the medicine?)

9. Your little brother thinks that ten is a very big number. He wants to play a dice game about the number ten. He proposes a game where you each start with a pile of candies, and he finds the sum of two dice several times. Whenever the sum is less than ten, he gives you one candy. Whenever the sum is ten or greater, you give him more than one candy—but he is not sure how many is fair. Help your brother finish inventing his game by using an expected value table to find how many candies must you give him when he "wins" so that the game has an expected value of zero.

10. Your friend is starting a food cart business. She has read that new food carts have a 35% chance to go out of business during the first year with a \$10,000 loss, a 30% chance to earn \$20,000 profit the first year, a 15% chance to earn \$30,000 profit the first year, a 15% chance to earn \$40,000 profit the first year, and a 5% chance to earn \$50,000 profit the first year. Assuming these numbers are true, and your friend has typical skill and luck in her new business, what is the expected value of her first year's income?

After you are very happy with your answers, turn in these Likelihood problems here.