Exam 9: Ratios, Rates, Proportions, and Percents

Make a sketch and give an explanation to illustrate this situation: Karen and Sara both jog. Sara jogged 2 1/2 miles, which is 2/3 as far as Karen jogged. How many miles did Karen jog?

Estimate each of the following and explain how you arrived at your estimate. A) 79% of $119 B) 0.5% of 89 kilograms C) 31% of 21,343 voters D) 121% of $29

Kathy owed her dad $80 and then paid off $24 from her tip earnings. A) What percent of the original debt had she paid? B) What percent was still owed? C) What was her new debt after the payment? The following evening, she paid him an additional $20 from her tip earnings. D) What percent of her new debt was paid off? E) What was her debt after the last payment? F) What percent of her original debt is now paid off?

There are four water slides at the Six Flags Atlantis water park. The following are the measurements of the four water slides. Which is the steepest slide, A, B, C, or D?

Use a three-column table to solve this problem. Label the columns Picture Frames, Cost, and Notes. If a box of 36 picture frames (all the same kind) costs $86.40, how much would five frames cost? (Assume no sale price, discount for volume, sales tax, etc.)

Ruben and Ofilia are painting the walls of a large lecture hall. They mixed 2 gallons of blue paint with 5 gallons of white paint for a total of 7 gallons of paint. They run out of paint. They estimate that they need 1/2 of a gallon to finish. A) Find the portion of the room that has been painted. Draw a neatly labeled diagram displaying your solution. B) If they mix 1/4 of a gallon of blue paint with 1 gallon of white paint, will the paint colors match? Explain your answer briefly. C) Suggest what amounts of blue paint and white paint would finish the room and match the color, perhaps with a little left over for touch-ups.

Felicia can run a mile in 4.7 minutes. Why is it not reasonable to treat a question about the time it takes her to run 8 miles as if it were a problem solved by proportions?

A child says that the two situations below would give the same "chocolateyness" since "each way has one more spoonful of chocolate sprinkles." Situation 1 3 spoonfuls of chocolate sprinkles on 2 scoops of vanilla ice cream Situation 2 4 spoonfuls of chocolate sprinkles on 3 scoops of vanilla ice cream Make a drawing (not just calculations) that would help the child see that the "chocolateyness" in the two situations would be different. (Use words as needed.)

A friend needs a serious operation and is considering two hospitals that have the following records for the surgery: Successes Failures Hospital A 20 8 Hospital B 50 18 The friend sees that B has more successes, but A has fewer failures and asks you for help in deciding. What will you say?

Terry uses 1 cup of Mr. Spiffy in $1 \frac { 1 } { 2 }$ gallons of water to clean the kitchen floor. What percent of the cleaning solution is Mr. Spiffy? (Note: 16 cups = 1 gallon.)

Gala apples are on sale today at $1.30 per pound. This is a discount of 30%. What was the cost before the sale?

John drives 7 3/10 miles to campus each day, while Vaneta drives only 4 miles to campus. John drives how many times as far as Vaneta?

Clarissa runs 240 meters in 45 seconds; Doña runs 160 meters in half a minute. Who runs faster?

If this box represents 75% of something, illustrate 125% of the same thing.

Make a sketch and give an explanation to illustrate this situation: After a bake sale, there were three identical white cakes left. You and your friend split them, but you took only a quarter as much as your friend took. Label your part M (for "me") and your friend's part F. How much of a cake (or how many cakes) did your friend take? (Give the numerical answer that makes sense here and add an explanation if the numerical answer is not clear from your sketch.)

The NASDAQ closed at 1590 today, down by 0.09%. What was the NASDAQ number at yesterday's closing?

If the Browns were to save an additional $14,000, they would have 1 2/5 times as much money as the amount the Joneses have in their savings account. The Joneses have $65,000. How much do the Browns currently have in their savings account?

A pollster noticed that, for every 40 men who were in favor of X, there were 28 women who were in favor of X. According to these figures, if 280 men were in favor of X, how many women were in favor of X?

Two painters on a large project want to paint different areas the same color. Painter A mixes 3 quarts of red paint with 2 gallons of white paint, and painter B mixes 5 quarts of the same kind of red paint with 4 gallons of white paint. Painter A says the two mixtures will be the same color, and painter B says his mixture will be redder than painter A's. Explain the thinking of each painter. Which one, if either, is correct? Explain your decision.

A machine can make 700 bolts in 40 minutes. At that rate, how many bolts can the machine make in one hour?