If A represents the number of apples purchased at 15 cents each, and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases in cents?

a) A+B
b) 25(A+B)
c)10A+15B
d) 15A+10B

To find the total value of the purchases in cents, we need to determine the cost of the apples and bananas separately, and then add them together.

The cost of the apples is given as 15 cents each and the number of apples purchased is represented by A. Therefore, the cost of apples in cents can be calculated as: 15A.

The cost of the bananas is given as 10 cents each and the number of bananas purchased is represented by B. Therefore, the cost of bananas in cents can be calculated as: 10B.

To find the total value of the purchases, we add the cost of the apples and the cost of the bananas together: 15A + 10B.

Therefore, the correct option that represents the total value of the purchases is: d) 15A + 10B.