There were some lemons and pomegranates in Box N and Box P. In Box N, the ratio of the lemons to the number of pomegranates was 2 : 1. In Box P, the ratio of the number of lemons to the number of pomegranates was 3 : 1. There were 3 times as many fruits in Box N as in Box P. After another 64 pomegranates were put into Box P, the ratio of the number of lemons to the number of pomegranates in Box P became 1 : 3. How many fruits were there in Box N?

Box N		Box P
3x4 = 12 u		1x4 = 4 u
Lemons	Pomegranates	Lemons	Pomegranates
2x4	1x4	3	1
8 u	4 u	3 u	1 u

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

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

	Box N		Box P
	Lemons	Pomegranates	Lemons	Pomegranates
Before	8 u	4 u	3 u	1 u
Change				+ 64
After	8 u	4 u	1x3 = 3 u	3x3 = 9 u

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

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

8 u = 64

1 u = 64 ÷ 8 = 8

Number of fruits in Box N
= 8 u + 4 u
= 12 u
= 12 x 8
= 96

Answer(s): 96