Question

A case of fruit contains apples, oranges, and mangos. There are four times more as many oranges as mangos. There are three more apples than mangos. If the case has a total of 39 pieces, how many mangos are in the case?

Answer 1

To solve the word problem, we let m represent the number of mangos, and through setting up an algebraic equation, we find that there are 6 mangos in the case.

Step-by-step explanation:

The student's question involves solving an algebraic word problem. We need to find out how many mangos are in the case given the relationships described between the number of oranges, apples, and mangos and the total number of fruits.

Let m represent the number of mangos. According to the problem, there are four times as many oranges as mangos, which can be represented as 4m. There are three more apples than mangos, so we have m + 3 apples. The total number of fruits is the sum of the number of mangos, oranges, and apples, which equals 39 pieces.

The equation representing this situation is: m (mangos) + 4m (oranges) + (m + 3) (apples) = 39 (total fruits).

Combining like terms gives us m + 4m + m + 3 = 39, which simplifies to 6m + 3 = 39. To solve for m, we subtract 3 from both sides, yielding 6m = 36, and then divide by 6 to get m = 6. Therefore, there are 6 mangos in the case.