There were some pears and mangosteens in Box Y and Box Z. In Box Y, the ratio of the pears to the number of mangosteens was 5 : 1. In Box Z, the ratio of the number of pears to the number of mangosteens was 5 : 3. There were 3 times as many fruits in Box Y as in Box Z. After another 68 mangosteens were put into Box Z, the ratio of the number of pears to the number of mangosteens in Box Z became 1 : 4. How many fruits were there in Box Y?

Box Y		Box Z
3x8 = 24 u		1x8 = 8 u
Pears	Mangosteens	Pears	Mangosteens
5x4	1x4	5	3
20 u	4 u	5 u	3 u

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

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

	Box Y		Box Z
	Pears	Mangosteens	Pears	Mangosteens
Before	20 u	4 u	5 u	3 u
Change				+ 68
After	20 u	4 u	1x5 = 5 u	4x5 = 20 u

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

Number of mangosteens put into Box Z
= 20 u - 3 u
= 17 u

17 u = 68

1 u = 68 ÷ 17 = 4

Number of fruits in Box Y
= 20 u + 4 u
= 24 u
= 24 x 4
= 96

Answer(s): 96