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 second hour 25.5 kg of apples were sold, how many kilograms of apples will be sold during the fourth hour of operation?

Answer 1

3.825 kg apples.

Explanation:

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

We have been given that during the first hour of operation the farm stand owner sold 15% of the apples he had. Then the amount of sold apples will be:

`\text{The amount of sold apples during 1st hour}=(15)/(100)x=0.15x`

`\text{The amount of remaining apples after 1st hour}=x-0.15x`

`\text{The amount of remaining apples after 1st hour}=0.85x`

On the second hour he sold 20% of the remaining apples. So the amount of sold apples on the second hour will be 20% of 0.85x.

`\text{The amount of sold apples during 2nd hour}=0.85x*(20)/(100)`

`\text{The amount of sold apples during 2nd hour}=0.85x* 0.20`

`\text{The amount of sold apples during 2nd hour}=0.17x`

During the second hour 25.5 kg of apples were sold, so we can set up an equation as:

`25.5=0.17x`

`(25.5)/(0.17)=(0.17x)/(0.17)`

`150=x`

So, stand owner had initially 150 kg of apples.

`\text{The amount of remaining apples after 2nd hour}=0.85x-0.17x`

`\text{The amount of remaining apples after 2nd hour}=0.68x`

On the third hour he sold 25% of the remaining apples. So the amount of sold apples on the 3rd hour will be 25% of 0.68x

`\text{The amount of sold apples during 3rd hour}=0.68x*(25)/(100)`

`\text{The amount of sold apples during 3rd hour}=0.68x*0.25`

`\text{The amount of sold apples during 3rd hour}=0.17x`

`\text{The amount of remaining apples after 3rd hour}=0.68x-0.17x`

`\text{The amount of remaining apples after 3rd hour}=0.51x`

As remaining apples were sold 5% more each following hour.

`\text{The amount of sold apples during 4th hour}=0.51x*(5)/(100)`

`\text{The amount of sold apples during 4th hour}=0.51x*0.05`

`\text{The amount of sold apples during 4th hour}=0.0255x`

Let us substitute x=150 into above equation we will get,

`\text{The amount of sold apples during 4th hour}=0.0255*150`

`\text{The amount of sold apples during 4th hour}=3.825`

Therefore, 3.825 kg of apples were sold during the 4th hour.