Luke had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall W and the ratio of mangosteens to starfruits was 3 : 8. When he reached Stall X, he unloaded ¹¹₁₂ of the starfruits and some mangosteens from his van. The ratio of mangosteens to starfruits became 3 : 4. At Stall Y, 35 mangosteens and 32 starfruits were collected and the number of mangosteens to starfruits became the same.

1. How many fruits were there on his van after visiting Stall Y?
2. How many mangosteens were delivered to Stall X?

	Location	Mangosteens	Starfruits
Comparing mangosteens and starfruits at first	Stall W	3x6 = 18 u	8x6 = 48 u
Before 1	Stall W	18 u	12x4 = 48 u
Change 1	Stall X	- ?	- 11x4 = - 44 u
After 1	Stall Y	3 u	1x4 = 4 u
Before 2	Stall Y	3x1 = 3 u	4x1 = 4 u
Change 2	Stall Y	+ 35	+ 32
After 2	Stall Y	3 u + 35	4 u + 32

(a)
The number of starfruits after unloading at Stall X is repeated.  Make the number of starfruits left after unloading at Stall X the same.  LCM of 4 and 1 is 4.

The number of starfruits collected at Stall W is repeated.  Make the number of starfruits collected at Stall W the same by multiplying 8 by 6. 
 
The number of mangosteens and starfruits in the end is the same.

4 u + 32 = 3 u + 35
4 u - 3 u = 35 - 32

1 u = 3

Number of mangosteens on his van after collecting from Stall Y
= 3 u + 35
= 3 x 3 + 35
= 9 + 35
= 44

Number of fruits on his van after collecting from Stall Y
= 2 x 44 
= 88 

(b)
Number of mangosteens delivered to Stall X
= 18 u - 3 u
= 15 u
= 15 x 3
= 45

Answer(s): (a) 88; (b) 45