There were some persimmons and starfruits in Box X and Box Y. In Box X, the ratio of the persimmons to the number of starfruits was 3 : 1. In Box Y, the ratio of the number of persimmons to the number of starfruits was 3 : 1. There were 3 times as many fruits in Box X as in Box Y. After another 64 starfruits were put into Box Y, the ratio of the number of persimmons to the number of starfruits in Box Y became 1 : 3. How many fruits were there in Box X?

Box X		Box Y
3x4 = 12 u		1x4 = 4 u
Persimmons	Starfruits	Persimmons	Starfruits
3x3	1x3	3	1
9 u	3 u	3 u	1 u

The total number of fruits in Box X is repeated.  Make the total number of fruits in Box X the same.  LCM of 3 and 4 is 12.

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

	Box X		Box Y
	Persimmons	Starfruits	Persimmons	Starfruits
Before	9 u	3 u	3 u	1 u
Change				+ 64
After	9 u	3 u	1x3 = 3 u	3x3 = 9 u

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

Number of starfruits put into Box Y
= 9 u - 1 u
= 8 u

8 u = 64

1 u = 64 ÷ 8 = 8

Number of fruits in Box X
= 9 u + 3 u
= 12 u
= 12 x 8
= 96

Answer(s): 96