There were some oranges and apples in Container Y and Container Z. In Container Y, the ratio of the oranges to the number of apples was 3 : 1. In Container Z, the ratio of the number of oranges to the number of apples was 3 : 1. There were 2 times as many fruits in Container Y as in Container Z. After another 33 apples were put into Container Z, the ratio of the number of oranges to the number of apples in Container Z became 1 : 4. How many fruits were there in Container Y?

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

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

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

	Container Y		Container Z
	Oranges	Apples	Oranges	Apples
Before	6 u	2 u	3 u	1 u
Change				+ 33
After	6 u	2 u	1x3 = 3 u	4x3 = 12 u

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

Number of apples put into Container Z
= 12 u - 1 u
= 11 u

11 u = 33

1 u = 33 ÷ 11 = 3

Number of fruits in Container Y
= 6 u + 2 u
= 8 u
= 8 x 3
= 24

Answer(s): 24