To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at

Question

The figure presents the graph of a line in a coordinate plane, with the origin labeled O. The horizontal axis is labeled “Number of hours at job A,” and the numbers 5 through 20, in increments of 5, are indied. The vertical axis is labeled “Number of hours at job B,” and the numbers 5 and 10 are indied. The line begins on the vertical axis at 8, and slants downward and to the right until it ends on the horizontal axis at 16.

To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. The graph above represents all possible combinations of numbers of hours Avery could have worked at the two jobs to earn s dollars. What is the value of s ?

A.

128

B.

160

C.

200

D.

320

Accepted Answer

Choice B is correct. Avery earns $10 per hour working at job A. Therefore, if she works a hours at job A, she will earn dollars. Avery earns $20 per hour working at job B. Therefore, if she works b hours at job B, she will earn dollars. The graph shown represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn s dollars. Therefore, if she worked a hours at job A, worked b hours at job B, and earned s dollars from both jobs, the following equation represents the graph: , where s is a constant. Identifying any point from the graph and substituting the values of the coordinates for a and b , respectively, in this equation yield the value of s . For example, the point , where and , lies on the graph. Substituting 16 for a and 0 for b in the equation yields , or . Similarly, the point , where and , lies on the graph. Substituting 0 for a and 8 for b in the equation yields , or . Choices A, C, and D are incorrect. If the value of s is 128, 200, or 320, then no points on the graph will satisfy this equation. For example, if the value of s is 128 (choice A), then the equation becomes . The point , where and , lies on the graph. However, substituting 16 for a and 0 for b in yields , or , which is false. Therefore, doesn&rsquo;t satisfy the equation, and so the value of s can&rsquo;t be 128. Similarly, if (choice C) or (choice D), then substituting 16 for a and 0 for b yields and , respectively, which are both false.

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