Question

Ken is working this summer as part of a crew on a farm. He earned $\$8$ per hour for the first $10$ hours 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 $\$270$?

Answer 1

It is given that Ken saves $90\%$ of his earnings.

Amount need to be saved $=\$270$

Say, minimum amount need to be earned to save $\$270=\$x$

So, $90\%\text{of}x=\$270$

$\Rightarrow \frac{90}{100}\times x=\$270$

$\Rightarrow 90x=\$270\times 100=\$27000$

$\Rightarrow x=\frac{\$27000}{90}$

$\Rightarrow x=\$300$

So, he must earn $\$300$ to save $\$270$.

Ken earns $\$8$ per hour for first $10hours$

So, total earning in first $10hours=\$8\times 10=\$80$

Now, the remaining amount need to be saved $=\$300-\$80=\$220$

So, number of more hours Ken need to work $=\frac{\text{remaining amount need to be saved}}{\text{hourly rate}}$

$=\frac{\$220}{\$10/hour}=22hours$

Now, Ken must work for at least $22hours$ for the rest of the week.