There were some pomegranates and persimmons in Box E and Box F. In Box E, the ratio of the pomegranates to the number of persimmons was 6 : 1. In Box F, the ratio of the number of pomegranates to the number of persimmons was 4 : 3. There were 2 times as many fruits in Box E as in Box F. After another 78 persimmons were put into Box F, the ratio of the number of pomegranates to the number of persimmons in Box F became 1 : 4. How many fruits were there in Box E?

Box E		Box F
2x7 = 14 u		1x7 = 7 u
Pomegranates	Persimmons	Pomegranates	Persimmons
6x2	1x2	4	3
12 u	2 u	4 u	3 u

The total number of fruits in Box E is repeated.  Make the total number of fruits in Box E the same.  LCM of 2 and 7 is 14.

The total number of fruits in Box F at first is repeated.  Make the total number of fruits in Box F the same.  LCM of 1 and 7 is 7.

	Box E		Box F
	Pomegranates	Persimmons	Pomegranates	Persimmons
Before	12 u	2 u	4 u	3 u
Change				+ 78
After	12 u	2 u	1x4 = 4 u	4x4 = 16 u

Number of pomegranates in Box F remains unchanged.  Make the number of pomegranates in Box F the same.  LCM of 4 and 1 is 4.

Number of persimmons put into Box F
= 16 u - 3 u
= 13 u

13 u = 78

1 u = 78 ÷ 13 = 6

Number of fruits in Box E
= 12 u + 2 u
= 14 u
= 14 x 6
= 84

Answer(s): 84