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?

Explanation

90% of his earnings each week, so this week he will save 0.9(10x + 80) dollars. The inequality 0.9(10x + 80) ≥ 270 represents the condition that he will save at least $270 for the week. Factoring 10 out of the expression 10x + 80 gives 10(x + 8). The product of 10 and 0.9 is 9, so the inequality can be rewritten as 9(x + 8) ≥ 270. Dividing both sides of this inequality by 9 yields x + 8 ≥ 30, so x ≥ 22. Therefore, the least number of hours Ken must work the rest of the week to save at least $270 for the week is 22.