Question

During the first hour of operation the farm stand owner sold 15% of the apples he had. On the second hour he sold 20% of the remaining apples. On the third hour he sold 25% of the remaining apples, and so on, selling 5% more each following hour. If during the third hour he sold 34 kg of apples, how many kilograms of apples did he have initially?

Answer 1

Initially he had 200 kg of apples.

Explanation:

Let x kg be the amount of apples the farm stand initially had.

During the first hour of operation the farm stand owner sold 15% of the apples he had, then he sold
`0.15x` kg of apples and
`x-0.15x=0.85x` kg of apples left.

On the second hour he sold 20% of the remaining apples, then he sold
`0.20\cdot 0.85x=0.17x` kg of apples and
`0.85x-0.17x=0.68x` kg of apples left.

On the third hour he sold 25% of the remaining apples, then during the third hour he sold
`0.25\cdot 0.68x=0.17x` kg of apples.

If during the third hour he sold 34 kg of apples, then
`0.17x=34\Rightarrow x=(34)/(0.17)=200\ kg.`