There were some starfruits and pomegranates in Box U and Box V. In Box U, the ratio of the starfruits to the number of pomegranates was 1 : 1. In Box V, the ratio of the number of starfruits to the number of pomegranates was 3 : 1. There were 2 times as many fruits in Box U as in Box V. After another 32 pomegranates were put into Box V, the ratio of the number of starfruits to the number of pomegranates in Box V became 1 : 3. How many fruits were there in Box U?

Box U		Box V
2x4 = 8 u		1x4 = 4 u
Starfruits	Pomegranates	Starfruits	Pomegranates
1x4	1x4	3	1
4 u	4 u	3 u	1 u

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

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

	Box U		Box V
	Starfruits	Pomegranates	Starfruits	Pomegranates
Before	4 u	4 u	3 u	1 u
Change				+ 32
After	4 u	4 u	1x3 = 3 u	3x3 = 9 u

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

Number of pomegranates put into Box V
= 9 u - 1 u
= 8 u

8 u = 32

1 u = 32 ÷ 8 = 4

Number of fruits in Box U
= 4 u + 4 u
= 8 u
= 8 x 4
= 32

Answer(s): 32