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Prealgebra

6.2 Solve General Applications of Percent

Prealgebra6.2 Solve General Applications of Percent
  1. Preface
  2. 1 Whole Numbers
    1. Introduction
    2. 1.1 Introduction to Whole Numbers
    3. 1.2 Add Whole Numbers
    4. 1.3 Subtract Whole Numbers
    5. 1.4 Multiply Whole Numbers
    6. 1.5 Divide Whole Numbers
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  3. 2 The Language of Algebra
    1. Introduction to the Language of Algebra
    2. 2.1 Use the Language of Algebra
    3. 2.2 Evaluate, Simplify, and Translate Expressions
    4. 2.3 Solving Equations Using the Subtraction and Addition Properties of Equality
    5. 2.4 Find Multiples and Factors
    6. 2.5 Prime Factorization and the Least Common Multiple
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  4. 3 Integers
    1. Introduction to Integers
    2. 3.1 Introduction to Integers
    3. 3.2 Add Integers
    4. 3.3 Subtract Integers
    5. 3.4 Multiply and Divide Integers
    6. 3.5 Solve Equations Using Integers; The Division Property of Equality
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  5. 4 Fractions
    1. Introduction to Fractions
    2. 4.1 Visualize Fractions
    3. 4.2 Multiply and Divide Fractions
    4. 4.3 Multiply and Divide Mixed Numbers and Complex Fractions
    5. 4.4 Add and Subtract Fractions with Common Denominators
    6. 4.5 Add and Subtract Fractions with Different Denominators
    7. 4.6 Add and Subtract Mixed Numbers
    8. 4.7 Solve Equations with Fractions
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  6. 5 Decimals
    1. Introduction to Decimals
    2. 5.1 Decimals
    3. 5.2 Decimal Operations
    4. 5.3 Decimals and Fractions
    5. 5.4 Solve Equations with Decimals
    6. 5.5 Averages and Probability
    7. 5.6 Ratios and Rate
    8. 5.7 Simplify and Use Square Roots
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  7. 6 Percents
    1. Introduction to Percents
    2. 6.1 Understand Percent
    3. 6.2 Solve General Applications of Percent
    4. 6.3 Solve Sales Tax, Commission, and Discount Applications
    5. 6.4 Solve Simple Interest Applications
    6. 6.5 Solve Proportions and their Applications
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  8. 7 The Properties of Real Numbers
    1. Introduction to the Properties of Real Numbers
    2. 7.1 Rational and Irrational Numbers
    3. 7.2 Commutative and Associative Properties
    4. 7.3 Distributive Property
    5. 7.4 Properties of Identity, Inverses, and Zero
    6. 7.5 Systems of Measurement
    7. Key Terms
    8. Key Concepts
    9. Exercises
      1. Review Exercises
      2. Practice Test
  9. 8 Solving Linear Equations
    1. Introduction to Solving Linear Equations
    2. 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
    3. 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
    4. 8.3 Solve Equations with Variables and Constants on Both Sides
    5. 8.4 Solve Equations with Fraction or Decimal Coefficients
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  10. 9 Math Models and Geometry
    1. Introduction
    2. 9.1 Use a Problem Solving Strategy
    3. 9.2 Solve Money Applications
    4. 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem
    5. 9.4 Use Properties of Rectangles, Triangles, and Trapezoids
    6. 9.5 Solve Geometry Applications: Circles and Irregular Figures
    7. 9.6 Solve Geometry Applications: Volume and Surface Area
    8. 9.7 Solve a Formula for a Specific Variable
    9. Key Terms
    10. Key Concepts
    11. Exercises
      1. Review Exercises
      2. Practice Test
  11. 10 Polynomials
    1. Introduction to Polynomials
    2. 10.1 Add and Subtract Polynomials
    3. 10.2 Use Multiplication Properties of Exponents
    4. 10.3 Multiply Polynomials
    5. 10.4 Divide Monomials
    6. 10.5 Integer Exponents and Scientific Notation
    7. 10.6 Introduction to Factoring Polynomials
    8. Key Terms
    9. Key Concepts
    10. Exercises
      1. Review Exercises
      2. Practice Test
  12. 11 Graphs
    1. Graphs
    2. 11.1 Use the Rectangular Coordinate System
    3. 11.2 Graphing Linear Equations
    4. 11.3 Graphing with Intercepts
    5. 11.4 Understand Slope of a Line
    6. Key Terms
    7. Key Concepts
    8. Exercises
      1. Review Exercises
      2. Practice Test
  13. A | Cumulative Review
  14. B | Powers and Roots Tables
  15. C | Geometric Formulas
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
  17. Index

Learning Objectives

By the end of this section, you will be able to:
  • Translate and solve basic percent equations
  • Solve applications of percent
  • Find percent increase and percent decrease
Be Prepared 6.2

Before you get started, take this readiness quiz.

  1. Translate and solve: 3434 of xx is 24.24.
    If you missed this problem, review Example 4.105.
  2. Simplify: (4.5)(2.38).(4.5)(2.38).
    If you missed this problem, review Example 5.15.
  3. Solve: 3.5=0.7n.3.5=0.7n.
    If you missed this problem, review Example 5.43.

Translate and Solve Basic Percent Equations

We will solve percent equations by using the methods we used to solve equations with fractions or decimals. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now as a prealgebra student, you can translate word sentences into algebraic equations, and then solve the equations.

We'll look at a common application of percent—tips to a server at a restaurant—to see how to set up a basic percent application.

When Aolani and her friends ate dinner at a restaurant, the bill came to $80.$80. They wanted to leave a 20%20% tip. What amount would the tip be?

To solve this, we want to find what amount is 20%20% of $80.$80. The $80$80 is called the base. The amount of the tip would be 0.20(80),0.20(80), or $16$16 See Figure 6.6. To find the amount of the tip, we multiplied the percent by the base.

The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.
Figure 6.6 A 20%20% tip for an $80$80 restaurant bill comes out to $16.$16.

In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.

Example 6.14

What number is 35%35% of 90?90?

Try It 6.27

What number is 45%45% of 80?80?

Try It 6.28

What number is 55%55% of 60?60?

Example 6.15

125%125% of 2828 is what number?

Try It 6.29

150%150% of 7878 is what number?

Try It 6.30

175%175% of 7272 is what number?

In the next examples, we are asked to find the base.

Example 6.16

Translate and solve: 3636 is 75%75% of what number?

Try It 6.31

1717 is 25%25% of what number?

Try It 6.32

4040 is 62.5%62.5% of what number?

Example 6.17

6.5%6.5% of what number is $1.17?$1.17?

Try It 6.33

7.5%7.5% of what number is $1.95?$1.95?

Try It 6.34

8.5%8.5% of what number is $3.06?$3.06?

In the next examples, we will solve for the percent.

Example 6.18

What percent of 3636 is 9?9?

Try It 6.35

What percent of 7676 is 57?57?

Try It 6.36

What percent of 120120 is 96?96?

Example 6.19

144144 is what percent of 96?96?

Try It 6.37

110110 is what percent of 88?88?

Try It 6.38

126126 is what percent of 72?72?

Solve Applications of Percent

Many applications of percent occur in our daily lives, such as tips, sales tax, discount, and interest. To solve these applications we'll translate to a basic percent equation, just like those we solved in the previous examples in this section. Once you translate the sentence into a percent equation, you know how to solve it.

We will update the strategy we used in our earlier applications to include equations now. Notice that we will translate a sentence into an equation.

How To

Solve an application

  1. Step 1. Identify what you are asked to find and choose a variable to represent it.
  2. Step 2. Write a sentence that gives the information to find it.
  3. Step 3. Translate the sentence into an equation.
  4. Step 4. Solve the equation using good algebra techniques.
  5. Step 5. Check the answer in the problem and make sure it makes sense.
  6. Step 6. Write a complete sentence that answers the question.

Now that we have the strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we'll solve involve everyday situations, you can rely on your own experience.

Example 6.20

Dezohn and his girlfriend enjoyed a dinner at a restaurant, and the bill was $68.50.$68.50. They want to leave an 18%18% tip. If the tip will be 18%18% of the total bill, how much should the tip be?

Try It 6.39

Cierra and her sister enjoyed a special dinner in a restaurant, and the bill was $81.50.$81.50. If she wants to leave 18%18% of the total bill as her tip, how much should she leave?

Try It 6.40

Kimngoc had lunch at her favorite restaurant. She wants to leave 15%15% of the total bill as her tip. If her bill was $14.40,$14.40, how much will she leave for the tip?

Example 6.21

The label on Masao's breakfast cereal said that one serving of cereal provides 8585 milligrams (mg) of potassium, which is 2%2% of the recommended daily amount. What is the total recommended daily amount of potassium?

The figures shows the nutrition facts for cereal.
Try It 6.41

One serving of wheat square cereal has 77 grams of fiber, which is 29%29% of the recommended daily amount. What is the total recommended daily amount of fiber?

Try It 6.42

One serving of rice cereal has 190190 mg of sodium, which is 8%8% of the recommended daily amount. What is the total recommended daily amount of sodium?

Example 6.22

Mitzi received some gourmet brownies as a gift. The wrapper said each brownie was 480480 calories, and had 240240 calories of fat. What percent of the total calories in each brownie comes from fat?

Try It 6.43

Veronica is planning to make muffins from a mix. The package says each muffin will be 230230 calories and 6060 calories will be from fat. What percent of the total calories is from fat? (Round to the nearest whole percent.)

Try It 6.44

The brownie mix Ricardo plans to use says that each brownie will be 190190 calories, and 7070 calories are from fat. What percent of the total calories are from fat?

Find Percent Increase and Percent Decrease

People in the media often talk about how much an amount has increased or decreased over a certain period of time. They usually express this increase or decrease as a percent.

To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.

How To

Find Percent Increase.

Step 1. Find the amount of increase.

  • increase=new amountoriginal amountincrease=new amountoriginal amount

Step 2. Find the percent increase as a percent of the original amount.

Example 6.23

In 2011,2011, the California governor proposed raising community college fees from $26$26 per unit to $36$36 per unit. Find the percent increase. (Round to the nearest tenth of a percent.)

Try It 6.45

In 2011,2011, the IRS increased the deductible mileage cost to 55.555.5 cents from 5151 cents. Find the percent increase. (Round to the nearest tenth of a percent.)

Try It 6.46

In 1995,1995, the standard bus fare in Chicago was $1.50.$1.50. In 2008,2008, the standard bus fare was $2.25.$2.25. Find the percent increase. (Round to the nearest tenth of a percent.)

Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.

How To

Find percent decrease.

  1. Step 1. Find the amount of decrease.
    • decrease=original amountnew amountdecrease=original amountnew amount
  2. Step 2. Find the percent decrease as a percent of the original amount.

Example 6.24

The average price of a gallon of gas in one city in June 20142014 was $3.71.$3.71. The average price in that city in July was $3.64.$3.64. Find the percent decrease.

Try It 6.47

The population of one city was about 672,000672,000 in 2010.2010. The population of the city is projected to be about 630,000630,000 in 2020.2020. Find the percent decrease. (Round to the nearest tenth of a percent.)

Try It 6.48

Last year Sheila's salary was $42,000.$42,000. Because of furlough days, this year her salary was $37,800.$37,800. Find the percent decrease. (Round to the nearest tenth of a percent.)

Media Access Additional Online Resources

Section 6.2 Exercises

Practice Makes Perfect

Translate and Solve Basic Percent Equations

In the following exercises, translate and solve.

98.

What number is 45%45% of 120?120?

99.

What number is 65%65% of 100?100?

100.

What number is 24%24% of 112?112?

101.

What number is 36%36% of 124?124?

102.

250%250% of 6565 is what number?

103.

150%150% of 9090 is what number?

104.

800%800% of 2,2502,250 is what number?

105.

600%600% of 1,7401,740 is what number?

106.

2828 is 25%25% of what number?

107.

3636 is 25%25% of what number?

108.

8181 is 75%75% of what number?

109.

9393 is 75%75% of what number?

110.

8.2%8.2% of what number is $2.87?$2.87?

111.

6.4%6.4% of what number is $2.88?$2.88?

112.

11.5%11.5% of what number is $108.10?$108.10?

113.

12.3%12.3% of what number is $92.25?$92.25?

114.

What percent of 260260 is 78?78?

115.

What percent of 215215 is 86?86?

116.

What percent of 1,5001,500 is 540?540?

117.

What percent of 1,8001,800 is 846?846?

118.

3030 is what percent of 20?20?

119.

5050 is what percent of 40?40?

120.

840840 is what percent of 480?480?

121.

790790 is what percent of 395?395?

Solve Applications of Percents

In the following exercises, solve the applications of percents.

122.

Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25.$74.25. She wants to leave 16%16% of the total bill as a tip. How much should the tip be?

123.

When Hiro and his co-workers had lunch at a restaurant the bill was $90.50.$90.50. They want to leave 18%18% of the total bill as a tip. How much should the tip be?

124.

Trong has 12%12% of each paycheck automatically deposited to his savings account. His last paycheck was $2,165.$2,165. How much money was deposited to Trong's savings account?

125.

Cherise deposits 8%8% of each paycheck into her retirement account. Her last paycheck was $1,485.$1,485. How much did Cherise deposit into her retirement account?

126.

One serving of oatmeal has 88 grams of fiber, which is 33%33% of the recommended daily amount. What is the total recommended daily amount of fiber?

127.

One serving of trail mix has 6767 grams of carbohydrates, which is 22%22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

128.

A bacon cheeseburger at a popular fast food restaurant contains 2,0702,070 milligrams (mg) of sodium, which is 86%86% of the recommended daily amount. What is the total recommended daily amount of sodium?

129.

A grilled chicken salad at a popular fast food restaurant contains 650650 milligrams (mg) of sodium, which is 27%27% of the recommended daily amount. What is the total recommended daily amount of sodium?

130.

The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380380 calories, and 171171 calories are from fat. What percent of the total calories is from fat?

131.

The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190190 calories, and 114114 calories are from fat. What percent of the total calories is from fat?

132.

Emma gets paid $3,000$3,000 per month. She pays $750$750 a month for rent. What percent of her monthly pay goes to rent?

133.

Dimple gets paid $3,200$3,200 per month. She pays $960$960 a month for rent. What percent of her monthly pay goes to rent?

Find Percent Increase and Percent Decrease

In the following exercises, find the percent increase or percent decrease.

134.

Tamanika got a raise in her hourly pay, from $15.50$15.50 to $17.55.$17.55. Find the percent increase.

135.

Ayodele got a raise in her hourly pay, from $24.50$24.50 to $25.48.$25.48. Find the percent increase.

136.

Annual student fees at the University of California rose from about $4,000$4,000 in 20002000 to about $9,000$9,000 in 2014.2014. Find the percent increase.

137.

The price of a share of one stock rose from $12.50$12.50 to $50.$50. Find the percent increase.

138.

According to Time magazine (7/19/2011)(7/19/2011) annual global seafood consumption rose from 2222 pounds per person in 19601960 to 3838 pounds per person today. Find the percent increase. (Round to the nearest tenth of a percent.)

139.

In one month, the median home price in the Northeast rose from $225,400$225,400 to $241,500.$241,500. Find the percent increase. (Round to the nearest tenth of a percent.)

140.

A grocery store reduced the price of a loaf of bread from $2.80$2.80 to $2.73.$2.73. Find the percent decrease.

141.

The price of a share of one stock fell from $8.75$8.75 to $8.54.$8.54. Find the percent decrease.

142.

Hernando's salary was $49,500$49,500 last year. This year his salary was cut to $44,055.$44,055. Find the percent decrease.

143.

From 20002000 to 2010,2010, the population of Detroit fell from about 951,000951,000 to about 714,000.714,000. Find the percent decrease. (Round to the nearest tenth of a percent.)

144.

In one month, the median home price in the West fell from $203,400$203,400 to $192,300.$192,300. Find the percent decrease. (Round to the nearest tenth of a percent.)

145.

Sales of video games and consoles fell from $1,150$1,150 million to $1,030$1,030 million in one year. Find the percent decrease. (Round to the nearest tenth of a percent.)

Everyday Math

146.

Tipping At the campus coffee cart, a medium coffee costs $1.65.$1.65. MaryAnne brings $2.00$2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

147.

Late Fees Alison was late paying her credit card bill of $249.$249. She was charged a 5%5% late fee. What was the amount of the late fee?

Writing Exercises

148.

Without solving the problem 4444 is 80%80% of what number”, think about what the solution might be. Should it be a number that is greater than 4444 or less than 44?44? Explain your reasoning.

149.

Without solving the problem “What is 20%20% of 300?”300?” think about what the solution might be. Should it be a number that is greater than 300300 or less than 300?300? Explain your reasoning.

150.

After returning from vacation, Alex said he should have packed 50%50% fewer shorts and 200%200% more shirts. Explain what Alex meant.

151.

Because of road construction in one city, commuters were advised to plan their Monday morning commute to take 150%150% of their usual commuting time. Explain what this means.

Self Check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

After reviewing this checklist, what will you do to become confident for all objectives?

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