Carl bought 19 apples of 2 different varieties to make a pie. The total cost of the apples was $5.10. Granny Smith apples cost $0.25 each and Gala apples cost $0.30 each. How many of each type of apple did Carl buy?

Carl bough 12 $0.25 apples and 7 $0.30 apples.

Step-by-step explanation:

This problem can be solved by using the following calculation:

We are going to call A apples to those of $0.25 each, and B apples to those whose value is $0.30. If Carl had 19 A-type apples, he would have spent $4.75, as 0.25 x 19 is equal to 4.75. Every time we subtract an A-type apple and add a B-type one, the total cost will rise 5 cents, because 0.30 - 0.25 is equal to 0.05.

So, as with 19 0.25 apples the total cost would be of $4.75, and the total cost of the apples that Carl effectively bought was of $5.10, the difference of both situations would be of $0.35. As 35/5 is equal to 7, and 5 cents were going to be added each time a $0.30 apple was added and a $0.25 apple was substracted, we can affirm that, of those 19 apples effectively bought by Carl, 12 costed $0.25 (12 x 0.25 = 3) and 7 costed $0.30 (7 x 0.30 = 2.10), therefore reaching the total cost of $5.10 (3 + 2.10 = 5.10).