# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.04

## The Art of Interpreting Percent

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## Lesson 6

Goal: Students will appreciate that a percentage of one quantity can relate to another quantity and vice versa. This concept is important when comparing one quantity to another such as the savings of one person in relationship to the savings of another.

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### Whole Quantity as a Percentage of Another Quantity

Problem 1.A Sharrard and Leighton are saving money to purchase a motorcycle Sharrard has saved $250 and Leighton has saved $400. Express Leighton’s savings as a percentage of Sharrard’s savings.

Answer 1. A. Sharrard’s savings of $250 equals 100% therefore, 100/250 x $400 = 160%. Leighton’s savings is 160% of Sharrard’s savings. Leighton saved $150 more than Sharrard, which represents a savings of 60% more than Sharrard.

Problem 1. B.Express Sharrard’s savings as a percentage of Leighton’s savings.

Answer 1. B. Leighton’s savings of $400 equals 100% therefore,100/400 x $250 = 62.5%

Sharrard’s savings is 62.5% of Leighton’s savings. Sharrard saved $150 less than Leighton, which represents a savings of 37.5% less than Leighton.

Problem 2. A. Jackie and Erika are saving money to purchase a sailboat. Jackie saved $1,200 and her sister Erika saved $800. Express Jackie’s savings as a percentage of Erika’s savings.

Answer 2. A. Erika’s savings of $800 equals 100% therefore, 100/800 x $1,200 = 150%.

Jackie’s savings is 150% of Erika’s savings. Jackie saved $400 more than Erika which represents a savings of 50% more than Erika.

Problem 2. B. Express Erika’s savings as a percentage of Jacki’s savings.

Answer 2. B. Jacki’s savings of $1,200 equals 100% therefore,100/$1,200 x $800 = 66.7%. Erika’s savings is 66.7% of Jacki’s savings. Erika saved $400 less than Jackie, which represents a savings of 33.3% less than Jackie.

### Percentage Change

Goal: Students should be able to calculate a percentage change such as an increase or decrease of a given item. If the percentage change is an increase then add the percentage increase to 100 percent. Then multiply the new rate by the current price to obtain the new price. If the percentage change is a decrease then subtract the percentage decrease from 100 percent. Then multiply the new rate by the current price to obtain the new price.

Problem 3. If gas costs $1.85 per gallon and the gas prices increase by 4%, what is the new price of the gas?

Answer 3. Take 100% plus 4% = 104%

The resulting rate is 104% of $1.85 = 1.04 x $1.85 = $1.92 per gallon.

Problem 4. If gas costs $1.79 per gallon and the gas prices increase by 3%, what is the new price of the gas?

Answer 4. Take 100% plus 3% = 103%

The resulting rate is 103% of $1.79 = 1.03 x $1.79 = $1.84 per gallon.

Problem 5. If gas costs $1.97 per gallon and the gas prices decrease by 5%, what is the new price of the gas?

Answer 5. Take 100% less 5% = 95%

The resulting rate is 95% of $1.97 = 0.95 x $1.97 = $1.87 per gallon.

Problem 6. If gas costs $1.95 per gallon and the gas prices decrease by 7%, what is the new price of the gas?

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Answer 6. Take 100% less 7% = 93%

The resulting rate is 93% of $1.95 = 0.93 x $1.95 = $1.81 per gallon.

Problem 7. Antwayne wanted to purchase a basketball with an original price of $36. His mother said he could purchase it only if it was reduced by 12%. What price must the basketball become before Antwayne’s mother will allow him to purchase it?

Answer 7. Take 100% less 12% = 88%

The resulting rate is 88% of $36 = 0.88 x $36 = $31.68 for the basketball.

Problem 8. Chantelle was selling a hand knit sweater for $42. She claimed the price would increase by 15% in two weeks. What will be the new price in two weeks?

Answer 8. Take 100% plus 15% = 115%

The resulting rate is 115% of $42 = 1.15 x $42 = $48.3 for the sweater.
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### Simple Interest

Goals: The students will appreciate that interest is a sum of money earned or charged as a percentage of a given amount. Banks will pay a customer a rate of interest in the form of a percentage of money which the customer allows the bank to borrow. In addition, if one borrows money from a bank in the form of a loan. The borrower agrees to pay back the amount borrowed plus interest, which is an agreed upon percentage rate. In addition, the time period is usually specified, ie the term of the loan may be 1, 2, 5, or $15 years. Also, an individual may desire to put a large sum of money into a certificate of deposit, which yields higher than normal rates of interest, usually for more than two years. The formula for solving Simple Interest is as follows: Interest Earned = Money x Interest Rate x Time

Problem 9. Find the simple interest on $950 at 8% per year for 3 years.
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Answer 9. Interest Earned = $950 x 8% = $950 x 0.08 = $76/year

Interest Earned = $76 x 3 years = $228
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Problem 10. Find the simple interest on $1,578 at 5% per year for 8 years.

Answer 10. Interest Earned = $1,578 x 5% = $1,578 x 0.05 = $78.90/ year

Interest Earned = $78.90 x 8 years = $631.20

Problem 11. Find the simple interest on $1,460 at 3% per year for 9 months.

Answer 11. Interest Earned = $1,460 x 3% = $1,460 x 0.03 = $43.8

Interest Earned = $43.8 x 9/12 months = $32.85
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### Percent Problems

1. Forty fifth graders were planning a class trip. Half (1/2) of the students wanted to go to the movies.

A. What percent of the students wanted to go to the movies?

B. How many students wanted to go to the movies?

2. Sixty fifth graders were planning a class trip. Three fourths (3/4) of the students wanted to go the new Harry Potter movie.

A. What percent of the students wanted to see the Harry Potter movie?

B. How many students wanted to see the Harry Potter movie?

C. How many students did not want to see the Harry Potter movie?

3. One hundred sixth graders were planning a class trip. One half of the students wanted to go to Six Flags Amusement Park, one fourth of the students wanted to go bowling, the rest of the students wanted to have lunch and play games at the park.

A. What percent of the students wanted to go to Six Flags?

B. How many students wanted to go to Six Flags?

C. What percent of the students wanted to go bowling?

D. How many students wanted to bowling?

E. What percentage of the students wanted to have lunch and play games at the park?

F. How many students wanted to have lunch and play games at the park?

4. Express each fraction as a decimal and percent.

A. 8/100

B 35/100

C 76/100

D 43/100

E 69/100

F 97/100

5. Express each percentage as a fraction and then write the fraction in its simplest form.

A. 6%

B. 18%

C. 45%

E. 78%

F. 86%

G. 94

6. If 65 out of 125 students ride the bus to school, what percentage of the students ride the school bus?

7. Tanika walks to school 20 out of 25 mornings. Express this ratio as a lowest term fraction and a percentage.

8. Gerald washed 10 out of the 25 cars during a fund raiser. Express this ratio as a fraction and a percentage.

9. Cecil washed 2/3 of the cars during a fund raiser. If 30 cars were washed what percentage of the cars did Cecil wash?

10. Johnny is playing Super Nintendo with his friend Rahim. Johnny won 12 games and Rahim won 18 games. What percentage of the games has Rahim won?

11. Shawnice bought a pair of Nike sneakers for $35.00, tax was 5%.

A. How much tax did Shawnice pay?

B. What was the total cost for the sneakers plus the tax?

12. Taniqua bought a pair of jeans for $25.00, tax was 6%.

A. How much tax did Taniqua pay?

B. What was the total cost for the jeans plus the tax?

13. Kylon bought a Yankees sweatshirt on sale. The original price was $50.00, the discounted price was 15% off the original price.

A. How many dollars was the discount?

B. What amount did Kylon pay for the sweatshirt?

14. Allen bought a Michael Jordan T-shirt on sale. The original price was $30.00, the discounted price was 18% off of the original price.

A. How many dollars was the discount?

B. What amount did Allen pay for the T-shirt?

15. Dr. Carberry took her girls leadership group of 20 students to lunch. The bill for lunch was $200.00. Dr. Carberry was pleased with the service and wanted to leave a 20% tip.

A.How many dollars should Dr. Carberry leave as a tip for the waitress?

B.How much money will the lunch cost including the tip?

16. Jack and Jill are playing marbles together. Jack has 35 green marbles and Jill has 60 red marbles; together they have 95 marbles. If Jack wins 25% percent of Jill’s marbles, how many marbles will Jill have?

17. Kendall brings $2.69 to the local toy store. She wants to buy a “Super Ball”. The ball costs $2.50 plus six percent sales tax. Does Kendall have enough money to buy the “Super Ball”?

18. JRMS boys basketball team played a game against West Haven. The total number of points scored by JRMS was 28. West Haven scored only 50% as many points as JRMS

A. How many points did West Haven score?

B. How many more points did JRMS score than West Haven?

19. JRMS girls basketball team played East Haven. JRMS scored 56 points and East Haven scored 25% as many points as JRMS.

A. How many points did East Haven score?

B. How many more points did JRMS score than East Haven?

20. One student gave her teacher a bouquet of flowers. There were 10 red carnations, 18 pink carnations, 5 yellow carnations and 7 daffodils. How many of the total flowers, to the nearest whole percent, were pink carnations?

21. At a gymnastics meet 65 medals were given to exceptional performers. There were

22 silver medals and 17 gold medals. The balance of the medals were bronze. What percentage of the medals were bronze?

22. Marty found a CD player on sale for $45 off of the original price, which represents a discount of 15%. What was the original price?

23. On the last day of school before Christmas, Julie brought 25 candy canes to her class. At the end of the day, 14 of the candy canes have been eaten, what percent are left?

24. Tim, Jim and Tom are all sharing a big blueberry pie. Tim takes the first slice and ends up taking 20 percent of the pie. Jim then takes 50 percent of the remaining amount of pie. What percent of the pie does Tom get?

25. Tyler, James, and Ralph share a pizza. Tyler takes the first slice, which is 40 percent of the pizza. James takes 30 percent of the remaining amount of the pizza. What percent of the pizza is left for Ralph?

26.Joshua spends 35 percent of his weekly allowance on entertainment, 45 percent on eating out, and 8 percent on new clothes. He saves the balance of his allowance, what percentage does he save each week?

27. Using the information from #26 and assuming Joshua has $50.00 from his allowance.

A. How much money does Joshua spend on entertainment?

B. How much money does Joshua save from his $50.00 in allowance?

28. At the New Haven Hotel 108 rooms have window views which represents 80% of the rooms. The rest of the rooms have views of the hallway. How many rooms do not have window views?

29. Lauren bought a pair of roller blades with an original price of $56.00. She was able to reduce the cost by 15% by using her discount coupon. How much money did Lauren pay for the roller blades?

30. Marcus bought a skate board on sale for $38.40, it was originally $48.00. What percentage was the discount?

31. Miles correctly answered 90% of the 80 questions on a math test. Jordan correctly answered 85% of the questions on the same test. How many more questions did Miles answer correctly.

32. Elena found a designer purse on sale, for 30% off the regular price of $19.95. The same purse is selling for $15.50 at a local boutique. Which purse is less expensive and by how much?

33. Cordell was planning to purchase a digital camera and began to comparison shop. At the camera shop the model he preferred was 25% off the original price of $124.00.

Then Cordell found a coupon which allowed him to take an additional15% off of the reduced price.

A. Is the discounted price more or less than $75.00 and by how much?

B. Is taking 25% and 15% the same as taking 40%? Explain?

34. Allen and Mustafa are saving money to purchase a go-cart. Allen has saved $75 and

Mustafa has saved $50.

A. Express Allen’s savings as a percentage of Mustafa’s savings.

B. Express Mustafa’s savings as a percentage of Allen’s.

35. Michale and Quaniesha are saving money to purchase a puppy. Quaniesha has saved

$65 and Michale has saved $105.

A. Express Quaniesha’s savings as a percentage of Michale’s savings.

B. Express Michale’s savings as a percentage of Quaniesha’s savings.

36. August and Taylor are saving money to attend a Mets game. August has saved $65 and Taylor has saved $35. August claims that she has saved 50% more than Taylor, is August correct?

37. If gas costs $1.87 per gallon and the gas prices increase by 6%, what is the new price of the gas?

38. If gas costs $1.77 per gallon and the gas prices decrease by 8%, what is the new price of the gas?

39. Angeline saw a backpack for $35 and the price decreased by 5% on sale, what is the new price of the backpack?

40. Carlos wanted to purchase a baseball cap for $23, the price was going to increase by 5% in one week. How much will the baseball cap cost in one week?

41. Mary wanted to deposit $450 in the bank at an interest rate of 5% for one year. How much interest will Mary earn in one year?

42.Calvin deposited $1,980 in a certificate of deposit at an interest rate of 7% for 3 years.

A. How much interest will Calvin earn in three years?

B. How much money will Calvin have including interest in three years?

43. Marcus borrowed $4,500 from a local bank at a 12% interest rate for 9 months.

How much interest will Marcus have to pay the bank after 9 months?

### TABLE VIII NUMBER LINE

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0 1/2 2/2

0 1/3 2/3 3/3

0 1/4 2/4 3/4 4/4

0 1/5 2/5 3/5 4/5 5/5

0 1/6 2/6 3/6 4/6 5/6 6/6

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

0 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10

0 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 12/12

@1H: TABLE IX METRIC MEASUREMENT 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 meter

0 1 2 3 4 5 6 7 8 9 10 dm

0 10 20 30 40 50 60 70 80 90 100 cm

Key: 1 m (meter) = 10 dm (decimeters) = 100 cm (centimeters)

### TABLE X METRIC MEASUREMENT

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

0 1 2 3 4 5 6 7 8 9 10 meters

0 1/2 2/2

0 1/3 2/3 3/3

0 1/4 2/4 3/4 4/4

0 1/5 2/5 3/5 4/5 5/5

0 1/6 2/6 3/6 4/6 5/6 6/6

0 1/8 2/8 3/8 4/8 5/8 6/8 7/8 8/8

0 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 10/10

0 1/12 2/12 3/12 4/12 5/12 6/12 7/12 8/12 9/12 10/12 11/12 12/12

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