If a represent the number of apples purchased at 15 cents each, and b represents the number of bananas purchased at 10 cent each, which of following represents the total value of the purchases in cents ?

We have A number of apples, each purchased at 15 cents.
We can, thus, calculate the total cost of apples as follows:
Total cost of apples = 15A cents

We have B number of bananas, each purchased at 10 cents.
We can, thus, calculate the total cost of bananas as follows:
Total cost of bananas = 10B cents

Now, the total cost of purchases can be calculated by adding the amount paid for  both types (apples and bananas) as follows:
Total cost = cost of apples + cost of bananas = 15A + 10B cents