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

Answer:

 3.825 kg apples.

Step-by-step 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:

$\text{The amount of sold apples during 1st hour}=\frac{15}{100}x=0.15x$

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

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

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.

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

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

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

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

$25.5=0.17x$

$\frac{25.5}{0.17}=\frac{0.17x}{0.17}$

$150=x$

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

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

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

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

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

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

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

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

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

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

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.