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

200 kg

Explanation:

First hour he sold 15% (remaining is 85%)

Second hour he sold 20% of remaining (which is 85%) -- so he sold
`(0.2)(0.85)=0.17`, which is 17% (remaining 85-17=68%)

Third hour he sold 25% of remaining (which is 68%) -- so he sold
`(0.25)(0.68)=17`, which is 17%

In third hour he sold 34, so 17% is 34. To find total he initially had, we need to find (100%). We can setup the ratio (letting x equal his initial amount):

`(0.17)/(34)=(1)/(x)\\0.17x=34\\x=(34)/(0.17)=200`

Initially the farm stand owner had 200 kg of apples.