There were some persimmons and pears in Container Q and Container R. In Container Q, the ratio of the persimmons to the number of pears was 6 : 1. In Container R, the ratio of the number of persimmons to the number of pears was 5 : 2. There were 3 times as many fruits in Container Q as in Container R. After another 16 pears were put into Container R, the ratio of the number of persimmons to the number of pears in Container R became 1 : 2. How many fruits were there in Container Q?

Container Q		Container R
3x7 = 21 u		1x7 = 7 u
Persimmons	Pears	Persimmons	Pears
6x3	1x3	5	2
18 u	3 u	5 u	2 u

The total number of fruits in Container Q is repeated.  Make the total number of fruits in Container Q the same.  LCM of 3 and 7 is 21.

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

	Container Q		Container R
	Persimmons	Pears	Persimmons	Pears
Before	18 u	3 u	5 u	2 u
Change				+ 16
After	18 u	3 u	1x5 = 5 u	2x5 = 10 u

Number of persimmons in Container R remains unchanged.  Make the number of persimmons in Container R the same.  LCM of 5 and 1 is 5.

Number of pears put into Container R
= 10 u - 2 u
= 8 u

8 u = 16

1 u = 16 ÷ 8 = 2

Number of fruits in Container Q
= 18 u + 3 u
= 21 u
= 21 x 2
= 42

Answer(s): 42