Ken is working this summer as part of a crew on a farm. He earned $\$ 8$ per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $\$ 10$ per hour for the rest of the week. Ken saves $90 \%$ of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $\$ 270$ for the week?
SAT · Math · previous-year question
- A.38
- B.33
- C.22correct
- D.16
Answer
C. 22
Explanation
Choice $\mathbf{C}$ is correct. Ken earned $\$ 8$ per hour for the first 10 hours he worked, so he earned a total of $\$ 80$ for the first 10 hours he worked. For the rest of the week, Ken was paid at the rate of $\$ 10$ per hour. Let $x$ be the number of hours he will work for the rest of the week. The total of Ken's earnings, in dollars, for the week will be $10 x+80$. He saves $90 \%$ of his earnings each week, so this week he will save $0.9(10 x+80)$ dollars. The inequality $0.9(10 x+80) \geq 270$ represents the condition that he will save at least $\$ 270$ for the week. Factoring 10 out o
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