There were some starfruits and lemons in Box S and Box T. In Box S, the ratio of the starfruits to the number of lemons was 5 : 1. In Box T, the ratio of the number of starfruits to the number of lemons was 5 : 3. There were 3 times as many fruits in Box S as in Box T. After another 34 lemons were put into Box T, the ratio of the number of starfruits to the number of lemons in Box T became 1 : 4. How many fruits were there in Box S?

Box S		Box T
3x8 = 24 u		1x8 = 8 u
Starfruits	Lemons	Starfruits	Lemons
5x4	1x4	5	3
20 u	4 u	5 u	3 u

The total number of fruits in Box S is repeated.  Make the total number of fruits in Box S the same.  LCM of 3 and 6 is 24.

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

	Box S		Box T
	Starfruits	Lemons	Starfruits	Lemons
Before	20 u	4 u	5 u	3 u
Change				+ 34
After	20 u	4 u	1x5 = 5 u	4x5 = 20 u

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

Number of lemons put into Box T
= 20 u - 3 u
= 17 u

17 u = 34

1 u = 34 ÷ 17 = 2

Number of fruits in Box S
= 20 u + 4 u
= 24 u
= 24 x 2
= 48

Answer(s): 48