Section 1.3 Homework questions?

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Section

Concepts

1.3 Applications of Linear Equations: Introduction to Problem Solving

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1. Translations Involving Linear Equations

2. Problem-Solving Strategies

3. Applications of Linear Equations

Translating Sentences in Equations(key words and phrases to remember)

Addition Subtraction Multiplication Division Powers

sum minus times quotient square 2

plus difference of divided by cube 3

total less than by ratio

more than less product

increased by decreased by twice

added to subtracted from

is → =

Example 1 Translating to a Linear Equation

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The sum of a number and negative eleven is negative fifteen. Find the number.

Example 2 Translating to a Linear Equation

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Forty less than five times a number is fifty-two less than the number. Find the number.

Example Translating to a Linear Equation

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Twice the sum of a number and six is two more than three times the number. Find the number.

3

Example 4 You Try

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a. The sum of a number and negative seven is 12. Find the number.

b. Thirteen more than twice a number is 5 more than the number. Find the number.

c. Three times the sum of a number and eight is 4 more than the number. Find the number.

Example 4 You Try

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a. The sum of a number and negative seven is 12. Find the number.

Example 4 You Try

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b. Thirteen more than twice a number is 5 more than the number. Find the number.

Example 4 You Try

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c. Three times the sum of a number and eight is 4 more than the number. Find the number.

Section 1.3 Applications of Linear Equations: Introduction to Problem Solving

2. Problem-Solving Strategies

(continued)

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Problem-Solving Flowchart for Word Problems

Section 1.3 Applications of Linear Equations: Introduction to Problem Solving

2. Problem-Solving Strategies

(continued)

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Section 1.3 Applications of Linear Equations: Introduction to Problem Solving

2. Problem-Solving Strategies

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Example 5 Using a Linear Equation in an Application

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The hit movie The Dark Knight set a record for grossingthe most money during its opening weekend. Thisamount surpassed the previous record set by the movieSpider-Man 3 by $4.2 million. The revenue from thesetwo movies was $306.4 million. How much revenue dideach movie bring in during its opening weekend?

3. Applications of Linear Equations

ExampleSolution:

5 Using a Linear Equation in an Application

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Example 6 We Try

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A carpenter cuts a 6-ft board in two pieces. One piece must be three times as long as the other. Find the length of each piece.

Example 7 We Try

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There are 40 students in an algebra class. There are 4 more women than men. How many women and how many men are in the class?

Example 8 You Try

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A board is 86 cm in length and must be cut so that one piece is 20 cm longer than the other piece. Find the length of each piece.

Example 9 You Try

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Maria’s age is 15 years less than Orlando’s age. The sum of their ages is 29. Find their ages.

Example 10 You Try

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For a recent year, the number of men in the U.S. Senate totaled 4 more than five times the number of women. Find the number of men and the number of women in the Senate given that the Senate has 100 members.

Section

Concepts

1.3 Applications of Linear Equations: Introduction to Problem Solving

Slide 21Copyright (c) The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

1. Translations Involving Linear Equations

2. Problem-Solving Strategies

3. Applications of Linear Equations

Section 1.3 Applications of Linear Equations: Introduction to Problem Solving

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