Question

A cafeteria manager needs to know how many apple and bananas to order. She asked students to choose either an apple or a banana as their preferred fruit. The survey results show that of the students who responded 5/8 picked bananas. If 80 students picked bananas how many picked apples?

Answer 1

48

Explanation:

The fraction who picked apples is the rest of the students:

1 - 5/8 = 3/8

of them.

So the number who picked apples relative to the number who picked bananas is ...

apples/bananas = (3/8)/(5/8) = 3/5

Multiplying this by the number who picked bananas gives the number who picked apples:

apples = bananas · 3/5 = 80·3/5 = 48

48 students picked apples.

____

Alternate solution

Let "a" represent the number who picked apples. The ratio of banana choosers to the total is 5/8, and there were 80 who chose bananas. That gives rise to the equation ...

80/(80 +a) = 5/8

640 = 400 +5a . . . . . . multiply by 8(80+a) and simplify

240 = 5a . . . . . . . . . . . subtract 400

240/5 = a = 48 . . . . . . divide by 5

48 students picked apples.