LESSON 6 PRACTICE PROBLEM SOLUTIONS 1.

Fraction Decimal Percent

43

0.75

75%

38

0.375

37.5%

72100 =

1825

0.72

72%

1310

1.3

130%

27

0.286

28.6%

2a. ! = 0.15 ∙ 30 = 4.5 2b. ! = 0.075 ∙ 100 = 0.75 2c. ! = 1.5   ∙ 40 = 60 2d. ! = 0.128 ∙ 17.45 = 2.2336 ≈ 2.23 2e. ! = 1.43 ∙ 12 = 17.16

3a. 75! = 5                                                ! = !!"≈ 0.07

3b. 12! = 3.25                                    ! = !.!"

!"≈ 0.27

3c. 14! = 5.03                                ! = !.!"

!"≈ 0.36

3d. 125! = 42                            ! = !"

!"#≈ 0.34

3e. !

!! = 15                                        ! = 15 ÷ !

!= 15 ∙ !

!= 45

4. Determine the missing number in each of the following. Round to two decimals as needed. 4a. 6% of what number is 12?

0.06 ∙ ! = 12

! =120.06 = 200

4b. 82% of what number is 116?

0.82 ∙ ! = 116

! =1160.82 = 141.46

4c. 123% of what number is 25?

1.23 ∙ ! = 25

! =251.23 = 20.33

4d. 20 is 0.18% of what number? 20 = 0.0018 ∙ !

! =20

0.0018 = 11,111.11 4e. 120 is 125% what number?

120 = 1.25 ∙ !

! =1201.25 = 96

5. Determine the missing number in each of the following. Round to two decimals as needed. 5a. What is 5% of 25?

! = 0.05 ∙ 25

! = 1.25 5b. 0.01% of 12 is what number?

0.0001 ∙ 12 = !

! = .0012 5c. 123% of 100 is what number?

1.23 ∙ 100 = !

! = 123

5d. 12.56% of 72 is what number?

0.1256 ∙ 72 = !

! = 9.04

5e. 50% of 127 is what number?

0.50 ∙ 127 = !

! = 63.5 6. Determine the missing number in each of the following. Round to two decimals as needed. 6a. What % of 25 is 5?

! ∙ 25 = 5

! =525 = 0.2 = 20%

6b. 12 is what percent of 40?

12 = ! ∙ 40

! =1240 = 0.3 = 30%

6c. What percent of 32 is 48?

! ∙ 32 = 48

! =4832 = 1.5 = 150%

6d. 15 is what percent of 23?

15 = ! ∙ 23

! =1523 = 0.6522 = 65.22%

6e. 0.25 is what percent of 3?

0.25 = ! ∙ 3

! =0.253 = 0.0833 = 8.33%

7. Determine the percent increase or decrease for the change for each of the following: 7a. 12 to 15

!"!!"!"

= !!"= 0.25 = 25%  !"#$%&'%

7b. 22 to 18

22 − 1822 =

422 = 0.1818 = 18.18%  !"#$"%&"

7c. 30 to 60

60 − 3030 =

3030 = 1 = 100%  !"#$%&'%

7d. 120 to 90

120 − 90120 =

30120 = 0.25 = 25%  !"#$"%&"

7e. 90 to 100

100 − 9090 =

1090 = 0.1111 = 11.11%

8a. In a recent poll, 28% of the 730 individuals polled indicated that they would

vote purely Democratic in the next election. How many of the individuals would

vote a straight Democratic ticket?

GIVEN: 28% of the 730 individuals polled indicated that they would vote purely

Democratic in the next election.

GOAL: How many of the individuals would vote a straight Democratic ticket?

MATH WORK: First rewrite the equation you need to solve in the verbal form

learned in this section.

28% of 730 is what number?

Now write the associated equation and solve.

0.28 ∙ 730 = !

! = 204.4

Since this represents a number of people, we will round to the nearest whole

person, 204.

CHECK: This seems reasonable. Our number should be less than 730 because

we are finding a part of a whole.

FINAL ANSWER: 204 people would vote a straight Democratic ticket.

8b. If you decrease your daily intake of calories from 2500 to 1750, by what

percent do your daily calories decrease?

GIVEN: You decrease your daily intake of calories from 2500 to 1750

GOAL: What percent do your daily calories decrease?

MATH WORK: First rewrite this decrease problem as described in this lesson.

2500 to 1750

Now set this up as a percent decrease problem.

2500 − 17502500 =

7502500 = 0.3 = 30%  !"#$"%&"

CHECK: The decrease is less than 100%. 30% seems like a reasonable amount.

FINAL ANSWER: Your daily calories decreased by 30%.

8c. On a recent trip to Walmart, you bought $75.25 worth of goods and paid a total of $82.02. What was the rate of sales tax that you paid? GIVEN: You bought $75.25 worth of goods and paid a total of $82.02. GOAL: What was the rate of sales tax that you paid?

MATH WORK: First rewrite the equation you need to solve in the verbal form learned in this section.

82.02 is what percent of 75.25

Now rewrite in algebraic form.

82.02 = ! ∙ 75.25

! =82.0275.25 = 1.09 = 109%

Since 109% represents 100% of the cost of the goods + the percentage of sales tax on the cost of the goods, the tax is

109% ─ 100% = 9%.

CHECK: 9% seems like a reasonable sales tax rate. FINAL ANSWER: The sales tax rate was 9%. 8d. If you invest $5000 at simple interest of 8% per year for 6 years, how much money will you earn from interest? How much money will you have at the end of 6 years? GIVEN: You invest $5000 at simple interest of 8% per year for 6 years GOAL: How much money will you have at the end of 6 years? MATH WORK: First, we will use the simple interest formula to find the interest.

! = !"# The principal, P = $5000 The rate, r = 8% = 0.08 The time in years, t = 6

! = 5000 ∙ 0.08 ∙ 6 = 2400

Since we are asked to find how much money you have at the end of the 6 years, we will combine the interest with the principal.

$5000 + $2400 = $7400 CHECK: I will use estimation to check if my result is reasonable. 10% of $5000 is $500. This is a little bit more than the 8% I am earning. This would be $500 per year for 6 years or $3000. This is a bit more than the $2400 interest I found. This seems reasonable. FINAL ANSWER: I will have $7400 at the end of 6 years. 8e. In the U.S. Civil War, 750,000 people were estimated to have died. If that number represented 2.5% of the U.S. population of the day, how many people lived in the U.S. during the Civil War? If a war of that scale happened today and the same percentage of people died, how many people would be killed (assume U.S. population of 314,721,724 people). [Source: Smithsonian Magazine, November 2012, page 48] GIVEN: In the U.S. Civil War, 750,000 people were estimated to have died This number represents 2.5% of the U.S. population of the day Assume the current U.S. population of 314,721,724 people GOALS: 1. How many people lived in the U.S. during the Civil War? 2. If a war of that scale happened today and the same percentage of people died, how many people would be killed?

MATH WORK: GOAL 1: First rewrite the equation you need to solve in the verbal form learned in this section.

750,000 is 2.5% of what number

Now rewrite in symbolic form and solve the equation.

750,000 = 0.025 ∙ !

! =7500000.025 = 30,000,000  !"#!$"

GOAL 2: First rewrite the equation you need to solve in the verbal form learned in this section.

What is 2.5% of 314,721,724

Now rewrite in symbolic form and solve the equation.

! = 0.025 ∙ 314,721,724 = 7868043.1 Since we are referring to the number of people, we will round to the nearest whole person,

7,868,043 people

CHECK: The population during the civil war seems reasonable. It’s about one tenth of the current population. The percentage that would die today seems accurate. I can estimate by finding 2.5% of 300 million. This is 7.5 million which is a good approximation. FINAL ANSWER: Approximately 30 million people lived in the US during the time of the Civil War. If the same percentage of people died today that died in the Civil War, this would be approximately 7,868,043 people.