percents chapter questions - njctlcontent.njctl.org/courses/math/7th-grade/percents/...2015/02/19...

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Percents Chapter Questions

1. Explain the relationship between decimals, fractions and percents.

2. Explain the three types of percent problems and how to solve them

3. What is percent change and how is it determined?

4. How can you represent a percent equation algebraically?

5. Give an example of percent decrease.

6. Give an example of percent increase.


Percents Chapter Problems

Relating Fractions, Decimals and Percents

Classwork

1. Order the numbers from least to greatest

a. 0.18, 18.5%, 8

50, 0.018

b. 5%, 1

2, 0.005, 5

c. 1.21, 0.121%, 1.21%, 12.1

2. Express each decimal or percent as a fraction in lowest terms

a. 0. 3̅

b. 6.25

c. 4.3

d. 0.008

e. 0.19

f. 280%

g. 5%

h. 0.25%

i. 48.2%

j. 321

2%

3. Express each decimal or fraction as a percent

a. 0.67

b. 0.07

c. 0.019

d. 3.8

e. 7.038

f. 18

20

g. 8

500

h. 16

50

i. 32

7

j. 4

11

4. Express each fraction or percent as a decimal

a. 2

15

b. 13

16

c. 7

8

d. 3

4

e. 2

7

f. 115%

g. 27%

h. 48.2%

i. 0.3%

j. 223

4%


Homework

5. Order the numbers from least to greatest

a. 0.49, 13

25, 49.9%, 0.049

b. 0.8, 1

12, 0.008, 8%

c. 33.3, 33.3%, 3.33%, 0.33

6. Express each decimal or percent as a fraction in lowest terms

a. 0. 6̅

b. 4.75

c. 7.9

d. 0.0018

e. 0.73

f. 348%

g. 9%

h. 0.37%

i. 96.3%

j. 811

4%

7. Express each decimal or fraction as a percent

a. 0.12

b. 0.6

c. 0.981

d. 4.92

e. 1.234

f. 13

20

g. 12

1000

h. 37

50

i. 54

9

j. 5

7

8. Express each fraction or percent as a decimal

a. 6

15

b. 14

16

c. 5

6

d. 1

8

e. 2

9

f. 61%

g. 787%

h. 1.1%

i. 0.8%

j. 324%


Three Types of Percent Problems

Classwork

9. Complete each of the following

a. What is 94% of 44?

b. 40% of 151 is what amount?

c. Find 360% of 60.

d. What is 84% of 65?

e. Find 190% of 95.

f. 95 is 34% of what number?

g. 5% of what is 95.5?

h. 106 is 15% of what?

i. 24 is 120% of what amount?

j. 85.2 is 24% of what?

k. 11 is what percent of 150?

l. 18 is what percent of 15?

m. What percent of 68 is 32.1?

n. What percent of 93 is 22?

o. 92.2 is what percent of 156?

p. 10% of what is 50?

q. 19 is 24% of what?

r. 76.2 is what percent of 12?

s. 59% of 5 is what amount?

t. 133 is what percent of 146?

Homework

10. Complete each of the following

a. 40% of 102 is what?

b. What is 190% of 117?

c. 46% of 70 is what amount?

d. What number is 37% of 91.3?

e. Find 360% of 82.

f. 111 is 98% of what?

g. 57 is 15% of what?

h. 34% of what is 47?

i. 52.5 is 120% of what amount?

j. 4.6 is 59% of what number?

k. 39 is what percent of 58?

l. What percent of 16 is 75?

m. 68 is what percent of 96?

n. What percent of 59 is 65.2?

o. 55 is what percent of 95?

p. 150 is 400% of what number?

q. 93 is what percent of 138?

r. Find 38% of 31

s. What is 45% of 118.4?

t. 390% of what is 139?


Percent of Change

Classwork

11. Find the percent of change. Remember to state if it is an increase or a decrease. Round your

answers to the nearest tenth.

a. Original amount: 17; New amount: 23

b. Original amount: 93; New amount: 19

c. You purchase a stereo for $53 then sell it on Craigs List for $26.

d. From 23 to 89

e. Your baby sister grows from 29 inches to 49 inches.

f. From 32 feet to 13 feet

g. A bridge is retrofitted and can now hold more weight. It originally held 39 tons. It can now

hold 74 tons.

h. Your school went to block scheduling. Classes used to be 42 minutes long. They are now

91 minutes long.

Homework

12. Find the percent of change. Remember to state if it is an increase or a decrease. Round your

answers to the nearest tenth.

a. Original amount: 49; New amount: 30

b. Original amount: 52; New amount: 94

c. You purchase a painting for $55 then sell it on Ebay for $91.

d. From 59 to 87

e. Your dog loses weight. She originally weighed 62 pounds and now she weighs 51 pounds.

f. From 65 feet to 47 feet.

g. The amount of sugar in a soft drink is decreased from 68 grams to 11 grams.

h. The amount of time allowed for a test is changed from 20 minutes to 42 minutes.

Representing Percent Equations Algebraically

Classwork

13. You buy a pair of jeans for $55. This price represents a 15% increase from the price the store paid

for the jeans. How much did the store pay?

14. The population of your town decreased by 12% from last year to this year. If there are 12,540 people

in the town this year, how many were there last year?

15. A TV is on sale for $399, or 16% off. What was the original price of the phone? Write and solve an

equation to represent this situation.

16. Sales tax in Philadelphia is 8.5%. What is the price of your items before taxes if your final price is

$162.75.

17. Luke has $50 in a savings account. The simple interest rate is 10% per year. How much interest will

he earn in 2 years?

18. Jane put $100 into a savings account. After one year her balance was $105. If Jane did not add any

other money to the account, what was her annual interest rate?

Homework

19. You sell your stereo for $383.50 which is 18% more than you paid for it. What was the price you paid

for the stereo?

20. Your school’s population increased by 12% from last year to this year. If there are 1,624 students in

the school this year, what was the population last year?

21. A computer is on sale for $450.50, or 15% off. What was the original price of the computer? Write

and solve an equation to represent the situation.


22. You pay your bill at a restaurant and add 24% to the bill for tax and tip. If you pay $55.80, what was

the total for the bill?

23. Micah has $50 in his savings account. The simple interest rate is 5% per year. How much interest will

he earn in 1 year?

24. Hillary’s savings account accrues 4.5% interest annually. If she started with $100 in her account, and

did not add any other money. The account now has $109. How much time has passed?

Applied Percent of Decrease

Classwork

25. The population of your town was 14,500 people. The latest census indicates the population has

decreased by 18%. What is the current population of your town?

26. A shirt that costs $29.99 is on sale for 25% off. What is the sale price of the shirt?

27. Your bill at a restaurant is $109.99. Since you are a frequent customer, the manager offers you a

15% discount. What is the amount of your discount?

28. The original price of a microscope is $274.50. If you wait for it to go on sale for 30% off, what will the

sale price be?

29. You purchase a new car for $18,000. As soon as you drive it off the lot, it is considered a “used” car

and loses 10% of its value. What is the value of the car when you drive it off the lot?

30. A motorcycle is valued at $5,400. You buy it used for a 40% discount. What is the amount of money

you save by purchasing it used?

31. A camera is on sale for 20% off its price of $99.95. What is the sale price?

32. You have a coupon for 15% off the cost of an oil change. If the oil change is $15.95, how much will

you pay?

Homework

33. You have $20 and would like to purchase a sweater that is on sale for 35% off. The original price of

the sweater is $29.50. Can you afford to buy it on sale?

34. The population of a town in Vermont decreases during the winter by 22%. What is the population of

the town during the winter if its population during the summer is 17,425 people?

35. As an employee, you get a 40% discount on all clothing purchased in the store. How much will you

save if you purchase a jacket that sells for $399.99?

36. You can buy a moped for $6,000 brand new or you can buy one on Craigs List for a 5% discount.

What is the cost of the moped on Craigs List?

37. The new computer you want to buy costs $749.50. If you wait for it to go on sale for 17% off, what

will the sale price be?

38. Your new cell phone cost $425. After you drop it on the ground, it loses 35% of its value. What is the

value of your cell phone after you drop it?

39. You have a coupon for 15% off any item in the store. If you purchase an item that costs $33.95, how

much will you pay?

40. What is the sale price of a car that is on sale for 24% off its list price of $23,000?

Applied Percent of Increase

Classwork

41. A store purchases a sweater for $40 then marks the price up 75% before selling it. What is the price

of the sweater in the store?

42. Calculate an 18% tip on a $84 bill.

43. A car costs $34,500. How much sales tax will the customer pay if the tax rate is 7%?


44. A stadium is increasing its seating capacity by 35%. If the stadium currently holds 65,000 people,

how many will it be able to hold after construction?

45. The population of your town has grown by 8% over the last year. If the population one year ago was

25,000 people what is the current population?

46. You have $70 in your purse. Your bill at a restaurant is $58. Do you have enough money to leave an

18% tip?

47. What is the total cost of a $230 bicycle with 8% tax?

48. How much money do you spend on a $55 dinner with a 20% tip?

Homework

49. The wholesale price of an MP3 player is $250. The store marks it up 40% before putting it out on the

shelves. What is the price the customer pays?

50. Calculate an 18% tip on a $47 bill

51. A parrot costs $149.99. How much sales tax will the customer pay if the tax rate is 8%?

52. A school’s population is projected to increase by 11%. If the total number of students this year is

14,100, how many students should they expect next year?

53. You upgrade your computer so that its memory capacity increases by 34%. If your old memory

capacity was 18 megs, what is your new capacity?

54. You have $300 in your purse. Do you have enough money to buy a $280 game system with 8%

sales tax?

55. What is the total cost of a $65 outfit with 7% tax?

56. How much money will you spend on a $110 meal with 20% tip?

Real-life Application Problems

Classwork

57. A store owner pays $18 for a shirt. To cover expenses, she marks up the price 40%. What is the

selling price of the shirt?

58. You calculated an 18% tip to be $24. What was the cost of your meal?

59. Your waitress gives you a bill for $85. You want to leave an 18% tip and you have to pay 8% tax.

What is the total amount of money you spend on your meal?

60. What is the final cost of a new game that was originally $25 if it is on sale for 15% off and there is 7%

tax?

61. What is the original price on a jacket that sells for $124 after a 30% discount?

62. You purchase a $55 play ticket online and are charged a surcharge. Your total is now $59.50. What

percent is the surcharge?

63. 1,250 people were surveyed. 45% said they prefer chocolate ice cream. How many people prefer

chocolate ice cream?

64. A television is on sale for 15% off the original price of $1,400. When it doesn’t sell, the manager

marks it down another 10% off the sale price. What is the new sale price of the television?

Homework

65. A necklace costs a store owner $125 to purchase. The owner marks up the price 65%. What is the

selling price of the necklace?

66. After looking at your bill, you calculate an 18% tip to be $14. What was the original bill?

67. You have saved $220 to purchase a new bicycle. Can you afford to buy the bike with a 30% discount

if it costs $325 and you have to pay 7% tax?

68. How much money will you spend if your lunch bill is $28, you pay 8% tax and you leave an 18% tip?

69. What is the original price of a pair of shoes that sell for $95 after a 35% discount?


70. You purchase concert tickets from ebay for $115. Face value for the tickets is $85. What percent

more did you pay?

71. 520 out of 3,200 people surveyed said they prefer running for exercise. What percent prefer running?

72. A new cell phone is on sale for 35% off its original price of $445. When it doesn’t sell, it is marked

down another 15% off the sale price. What is the new sale price of the cell phone?


Answer Key

1.

a. 0.018, 8

50, 0.18, 18.5%

b. b. 0.005, 5%, ½ , 5

c. 0.121%, 1.21%, 1.21, 12.1

2.

a. 3

10

b. 61

4

c. 43

10

d. 1

125

e. 19

100

f. 24

5

g. 1

20

h. 1

400

i. 241

500

j. 13

40

3.

a. 67%

b. 7%

c. 1.9%

d. 380%

e. 703.8%

f. 90%

g. 1.6%

h. 32%

i. 328.57%

j. 36. 36̅̅̅̅ %

4.

a. 0.13̅

b. 0.8125

c. 0.875

d. 0.75

e. 0.2857

f. 1.15

g. 0.27

h. 0.482

i. 0.003

j. 0.2275

5.

a. 0.049, 0.49, 49.9%, 13

25

b. 0.008, 8%, 1

12, 0.8

c. 3.33%, 0.33, 33.3%, 33.3

6.

a. 2

3

b. 43

4

c. 79

10

d. 9

5000

e. 73

100

f. 312

25

g. 9

100

h. 37

10,000

i. 963

1,000

j. 13

16

7.

a. 12%

b. 60%

c. 98.1%

d. 492%

e. 123.4%

f. 65%

g. 1.2%

h. 74%

i. 544.4̅%

j. 71.428571%

8.

a. 0.4


b. 0.875

c. 0.83̅

d. 0.125

e. 0.2̅

f. 0.61

g. 7.87

h. 0.011

i. 0.008

j. 3.24

9.

a. 41.36

b. 60.4

c. 216

d. 54.6

e. 180.5

f. 279.41

g. 1910

h. 7062

3

i. 20

j. 355

k. 71

3%

l. 120%

m. 47.2%

n. 23.7%

o. 59.1%

p. 500

q. 79.16̅

r. 635%

s. 2.95

t. 91.1%

10.

a. 40.8

b. 222.3

c. 32.2

d. 33.781

e. 295.2

f. 113.26

g. 380

h. 138.24

i. 43.75

j. 7.797

k. 67.24%

l. 468.75%

m. 70.83%

n. 110.51%

o. 57.89%

p. 371

2 or 37.5

q. 67.39%

r. 11.78

s. 53.28

t. 35.64

11.

a. 35.3% increase

b. 79.6% decrease

c. 50.9% decrease

d. 287% increase

e. 68.97% increase

f. 59.4% decrease

g. 89.7% increase

h. 1162

3% increase

12.

a. 38.8% decrease

b. 80.8% increase

c. 65.5% increase

d. 47.5% increase

e. 17.7% decrease

f. 27.7% decrease

g. 83.8% decrease

h. 110% increase

13. 1x + 0.15x = 55; x=$47.83

14. 1x - 0.12x = 12,540; x=14,250 people last

year

15. 1x - 0.16x = 399; x=$475

16. 1x + 0.085x = 162.75; x=$150


17. $5

18. 5%

19. 1x + 0.18x = 383.5, x=$325

20. 1x + 0.12x = 1624; x=1,450 students last

year

21. 1x - .015x = 450.50; x=$530

22. 1x + 0.24x = 55.80; x=$45

23. $2.50

24. 2 years

25. 11,890

26. $22.49

27. $16.50

28. $192.15

29. $16,200

30. $2,160

31. $79.96

32. $13.56

33. Yes, it costs $19.18 on sale

34. 13,592 people

35. $160.00

36. $5,700

37. $622.09

38. $276.25

39. $28.86

40. $17,480

41. $70

42. $15.12

43. $2,415

44. 87,750 people

45. 27,000 people

46. Yes, total is $68.44

47. $248.40

48. $66

49. $350

50. $8.46

51. $12.00

52. 15,651 students

53. 24.12 megs

54. No, total is $302.40

55. $69.55

56. $132

57. $25.20

58. $133.33

59. $107.10 ($6.80 tax, $15.30 tip separately)

60. $22.74

61. $177.14

62. 8.18%

63. 562.5 people so 562 people

64. $1071

65. $206.25

66. $77.78

67. No, it will cost $243.43

68. $35.28 ($2.24 tax, $5.04 tip separately)

69. $146.15

70. 35.3%

71. 16.25% or 161

4%

72. $245.86


Percents Unit Review PMI 7th Grade Math Name ________________________ Multiple Choice– Choose the correct answer for each question. No partial credit will be given.

1) Write 0.4 as a percent. a. 0.04%

b. 0.4%

c. 40%

d. 400%

2) Write %4

32 as a decimal.

a. 75.2

b. 0.275

c. 275

d. 0275.

3) Write 15

43 as a percent.

a. 13.8%

b. .138%

c. 1380%

d. 138%

4) Write 136% as a fraction in lowest terms.

a. 25

36

b. 25

91

c. 25

613

d. 25

34

5) What is 1% of 100?

a. 0.1

b. 1

c. 10

d. .01


6) 7 is 42% of what number?

a. 6

b. 16.67

c. .06

d. 0.167

7) 52 is what percent of 60? (Round your answer to the nearest tenth of a percent).

a. 8670%

b. 86.7%

c. 115.4%

d. 1.154%

8) On a quiz, you answered 20 questions correctly out of 28. What percent did you answer correctly? (Round

your answer to nearest percent).

a. 28%

b. 29%

c. 71%

d. 72%

9) Find the percent of change from $20 to $15

a. 5% decrease

b. 5% increase

c. 25% decrease

d. 25% increase

10) Your bank account increased from 37 dollars to 82 dollars. Find the percent of change.

a. 121.6% increase

b. 121.6% decrease

c. 91.4% increase

d. 91.4% decrease

11) How much will you pay for a $165 bike if you have a coupon for 20% off?

a. $33

b. $198

c. $130

d. $132

12) If sales tax is 7%, how much tax will you pay for a $45 taxable item?

a. $31.50

b. $3.15

c. $41.85

d. $4.19

13) Your bill at a restaurant is $32. If you pay 7% tax and leave an 18% tip, how much money do you spend?

(Do not tip on the tax and do not tax the tip!)

a. $37.76

b. $34.24

c. $40

d. $42.76


14) A coat that originally cost $90 went on sale for $55. What was the percent of discount?

a. 38.9%

b. 35%

c. 45%

d. 61%

15) A stereo is on sale for $275, after a 30% discount. What was the original price of the stereo?

a. $117.86

b. $392.86

c. $400

d. Can’t be determined

Short Constructed Response – Write the correct answer for each question. No partial credit will be given.

16) The cost of a donut increased from $0.55 to $0.75. What was the percent of increase? If necessary, round

your answer to the nearest tenth of a percent.

17) The cost of needed items at the auto supply store is $118.75. Sales tax is 7.25%. What is the total bill?

18) The 18% tip was $20. What was the amount before the tip? (Round your answer to the nearest dollar)

19) What percent of 50 is 140?

20) 60% of what is 300?

21) Reggie has a savings account that earns 5% interest per year. The only time he put money in the account

was the initial deposit. If the account has $44 after 2 years, what was his starting deposit?

22) Lawrence has $25,000 in his savings account that earns 13% annual interest. How much interest will he

accrue in 3 years?

Extended Constructed Response - Solve the problem, showing all work. Partial credit may be given.


23) Two stores are advertising the same bicycle. Store A has the bike priced at $160 + 20% off. Store B has the

bike priced at $185 + 25% off.

a. Determine the cost of the bike at Store A and Store B.

b. What store is offering the best price?

c. How much more would you have spent if you had purchased the bike at the other store?

24) Mark’s math average increased from 72 to 91. His parents told him that if he increased his average at least

20% they would buy him a phone.

a. How much did Mark’s average increase?

b. Did Mark get a phone?

c. What is the least amount that Mark’s average would have to increase so that he could get a phone?

25) A group of 4 students went to the diner after the school play. The waitress put the $56 receipt on the table.

The final total, including tip (18%) and tax (7%), was going to be evenly divided among the 4 students.

(Remember! Do not tip on the tax and do not tax the tip!). Round all answers to the nearest cent.

a. What was the tip?

b. What was the tax?

c. How much did each person pay?

26) A $24 shirt is on sale for 15% off. You have a coupon that will take an additional 10% off, after the first. Your

friend says, “Why don’t they just take 25% off? It’s the same amount!” She then adds, “Isn’t it?” How do you

respond? Justify your answer.


Percents Unit Review Answers

1. C

2. D

3. C

4. D

5. B

6. B

7. B

8. C

9. C

10. A

11. D

12. B

13. C

14. A

15. B

16. 36.4% increase

17. $127.36

18. $111.11

19. 280%

20. 500

21. $40

22. $9,750

23. A. Store A: $128

Store B: $138.75

b. Store A

c. $10.75 more

24. A. 26.4%

B. Yes

C. 14.4

23. A. 3.92

B. 10.08

C. 17.50

24. First option: $18.36

25% off: $18

The options are not the same. 25% off results in an additional savings of $0.36

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