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?

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:

[tex]\text{The amount of sold apples during 1st hour}=\frac{15}{100}x=0.15x[/tex]

[tex]\text{The amount of remaining apples after 1st hour}=x-0.15x[/tex]

[tex]\text{The amount of remaining apples after 1st hour}=0.85x[/tex]

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.

[tex]\text{The amount of sold apples during 2nd hour}=0.85x*\frac{20}{100}[/tex]

[tex]\text{The amount of sold apples during 2nd hour}=0.85x\times 0.20[/tex]

[tex]\text{The amount of sold apples during 2nd hour}=0.17x[/tex]

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

[tex]25.5=0.17x[/tex]

[tex]\frac{25.5}{0.17}=\frac{0.17x}{0.17}[/tex]

[tex]150=x[/tex]

So, stand owner had initially 150 kg of apples.

[tex]\text{The amount of remaining apples after 2nd hour}=0.85x-0.17x[/tex]

[tex]\text{The amount of remaining apples after 2nd hour}=0.68x[/tex]

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

[tex]\text{The amount of sold apples during 3rd hour}=0.68x*\frac{25}{100}[/tex]

[tex]\text{The amount of sold apples during 3rd hour}=0.68x*0.25[/tex]

[tex]\text{The amount of sold apples during 3rd hour}=0.17x[/tex]

[tex]\text{The amount of remaining apples after 3rd hour}=0.68x-0.17x[/tex]

[tex]\text{The amount of remaining apples after 3rd hour}=0.51x[/tex]

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

[tex]\text{The amount of sold apples during 4th hour}=0.51x*\frac{5}{100}[/tex]

[tex]\text{The amount of sold apples during 4th hour}=0.51x*0.05[/tex]

[tex]\text{The amount of sold apples during 4th hour}=0.0255x[/tex]

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

[tex]\text{The amount of sold apples during 4th hour}=0.0255*150[/tex]

[tex]\text{The amount of sold apples during 4th hour}=3.825[/tex]

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