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.

b) 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?

22.95 kg

Step-by-step explanation:

Let's say the farm stand owner starts with x kg of apples.

During the first hour, he sells 15% of the apples:

0.15 x

This means he's left with 85% of the original apples.  During the second hour, he sells 20% of the remaining apples:

0.20 (0.85 x)

= 0.17 x

He's sold a total of 15% + 17% = 32% of the apples, so he's left with 68% of the apples.  Continuing the pattern, the apples sold during the third hour:

0.25 (0.68 x)

= 0.17 x

He's sold 49% of the apples and is left with 51%.  The apples sold during the fourth hour:

0.30 (0.51 x)

= 0.153 x

If 0.17 x = 25.5, then x = 150.  So the apples sold during the fourth hour is:

0.153 (150) = 22.95