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**Writing Linear Models from Word Problems**

Coordinate Algebra A.CED.1

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Essential Question How do I create equations in one variable and use them to solve problems?

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Vocabulary A linear model is a linear equation that represents a real-world scenario.

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Example 1 A machine salesperson earns a base salary of $40,000 plus a commission of $300 for every machine he sells. Write an equation that shows the total amount of income the salesperson earns, if he sells x machines in a year. y = $300x + $40,000

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Example 2 The linear model that shows the total income for the salesperson in example 1 is y = 300x + 40,000. What would be the salesperson’s income if he sold 150 machines? Let x = (150) + 40,000 85,000

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Continued How many machines would the salesperson need to sell to earn a $100,000 income? Let y = 100,000 and solve for x 100,000 = 300x + 40,000 Subtract 40,000 60,000 = 300x Divide by 300 X = 200

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Example 3 At a school play, children’s tickets cost $3 each and adult tickets cost $7 each. The total amount of money earned from ticket sales equals $210. Write a linear model that relates the number of children’s tickets sold to the number of adult tickets sold. Let x = the number of children’s tickets sold and y = the number of adult tickets sold. 3x + 7y = 210

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Example 4 In the ticket sales example, how many children’s tickets were sold if 24 adult tickets were sold? 3x + 7y = 210 Write the linear model. 3x + 7(24) = 210 Substitute y = 24. 3x = 210 Simplify. Subtract. 3x = 42 Divide. x = 14

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Assignment: Worksheet!!

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Warm-Up: Problem of the Day Julie has dimes and quarters in her pocket. She has 24 coins in total. If the number of dimes is 3 less than twice the number.

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