There were some pomegranates and pears in Box K and Box L. In Box K, the ratio of the pomegranates to the number of pears was 11 : 1. In Box L, the ratio of the number of pomegranates to the number of pears was 5 : 3. There were 3 times as many fruits in Box K as in Box L. After another 56 pears were put into Box L, the ratio of the number of pomegranates to the number of pears in Box L became 1 : 2. How many fruits were there in Box K?

Box K		Box L
3x8 = 24 u		1x8 = 8 u
Pomegranates	Pears	Pomegranates	Pears
11x2	1x2	5	3
22 u	2 u	5 u	3 u

The total number of fruits in Box K is repeated.  Make the total number of fruits in Box K the same.  LCM of 3 and 12 is 24.

The total number of fruits in Box L at first is repeated.  Make the total number of fruits in Box L the same.  LCM of 1 and 8 is 8.

	Box K		Box L
	Pomegranates	Pears	Pomegranates	Pears
Before	22 u	2 u	5 u	3 u
Change				+ 56
After	22 u	2 u	1x5 = 5 u	2x5 = 10 u

Number of pomegranates in Box L remains unchanged.  Make the number of pomegranates in Box L the same.  LCM of 5 and 1 is 5.

Number of pears put into Box L
= 10 u - 3 u
= 7 u

7 u = 56

1 u = 56 ÷ 7 = 8

Number of fruits in Box K
= 22 u + 2 u
= 24 u
= 24 x 8
= 192

Answer(s): 192