There were some apples and mangosteens in Box F and Box G. In Box F, the ratio of the apples to the number of mangosteens was 3 : 1. In Box G, the ratio of the number of apples to the number of mangosteens was 3 : 1. There were 3 times as many fruits in Box F as in Box G. After another 16 mangosteens were put into Box G, the ratio of the number of apples to the number of mangosteens in Box G became 1 : 3. How many fruits were there in Box F?

Box F		Box G
3x4 = 12 u		1x4 = 4 u
Apples	Mangosteens	Apples	Mangosteens
3x3	1x3	3	1
9 u	3 u	3 u	1 u

The total number of fruits in Box F is repeated.  Make the total number of fruits in Box F the same.  LCM of 3 and 4 is 12.

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

	Box F		Box G
	Apples	Mangosteens	Apples	Mangosteens
Before	9 u	3 u	3 u	1 u
Change				+ 16
After	9 u	3 u	1x3 = 3 u	3x3 = 9 u

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

Number of mangosteens put into Box G
= 9 u - 1 u
= 8 u

8 u = 16

1 u = 16 ÷ 8 = 2

Number of fruits in Box F
= 9 u + 3 u
= 12 u
= 12 x 2
= 24

Answer(s): 24