There were some apples and oranges in Box Y and Box Z. In Box Y, the ratio of the apples to the number of oranges was 3 : 1. In Box Z, the ratio of the number of apples to the number of oranges was 3 : 1. There were 2 times as many fruits in Box Y as in Box Z. After another 40 oranges were put into Box Z, the ratio of the number of apples to the number of oranges in Box Z became 1 : 2. How many fruits were there in Box Y?

Box Y		Box Z
2x4 = 8 u		1x4 = 4 u
Apples	Oranges	Apples	Oranges
3x2	1x2	3	1
6 u	2 u	3 u	1 u

The total number of fruits in Box Y is repeated.  Make the total number of fruits in Box Y the same.  LCM of 2 and 4 is 8.

The total number of fruits in Box Z at first is repeated.  Make the total number of fruits in Box Z the same.  LCM of 1 and 4 is 4.

	Box Y		Box Z
	Apples	Oranges	Apples	Oranges
Before	6 u	2 u	3 u	1 u
Change				+ 40
After	6 u	2 u	1x3 = 3 u	2x3 = 6 u

Number of apples in Box Z remains unchanged.  Make the number of apples in Box Z the same.  LCM of 3 and 1 is 3.

Number of oranges put into Box Z
= 6 u - 1 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Number of fruits in Box Y
= 6 u + 2 u
= 8 u
= 8 x 8
= 64

Answer(s): 64