There were some persimmons and apples in Box W and Box X. In Box W, the ratio of the persimmons to the number of apples was 1 : 1. In Box X, the ratio of the number of persimmons to the number of apples was 3 : 1. There were 2 times as many fruits in Box W as in Box X. After another 45 apples were put into Box X, the ratio of the number of persimmons to the number of apples in Box X became 1 : 2. How many fruits were there in Box W?

Box W		Box X
2x4 = 8 u		1x4 = 4 u
Persimmons	Apples	Persimmons	Apples
1x4	1x4	3	1
4 u	4 u	3 u	1 u

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

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

	Box W		Box X
	Persimmons	Apples	Persimmons	Apples
Before	4 u	4 u	3 u	1 u
Change				+ 45
After	4 u	4 u	1x3 = 3 u	2x3 = 6 u

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

Number of apples put into Box X
= 6 u - 1 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of fruits in Box W
= 4 u + 4 u
= 8 u
= 8 x 9
= 72

Answer(s): 72