Billy had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart G and the ratio of starfruits to lemons was 3 : 8. When he reached Mart H, he unloaded ¹¹₁₂ of the lemons and some starfruits from his van. The ratio of starfruits to lemons became 3 : 4. At Mart J, 57 starfruits and 49 lemons were collected and the number of starfruits to lemons became the same.

1. How many fruits were there on his van after visiting Mart J?
2. How many starfruits were delivered to Mart H?

	Location	Starfruits	Lemons
Comparing starfruits and lemons at first	Mart G	3x6 = 18 u	8x6 = 48 u
Before 1	Mart G	18 u	12x4 = 48 u
Change 1	Mart H	- ?	- 11x4 = - 44 u
After 1	Mart J	3 u	1x4 = 4 u
Before 2	Mart J	3x1 = 3 u	4x1 = 4 u
Change 2	Mart J	+ 57	+ 49
After 2	Mart J	3 u + 57	4 u + 49

(a)
The number of lemons after unloading at Mart H is repeated.  Make the number of lemons left after unloading at Mart H the same.  LCM of 4 and 1 is 4.

The number of lemons collected at Mart G is repeated.  Make the number of lemons collected at Mart G the same by multiplying 8 by 6. 
 
The number of starfruits and lemons in the end is the same.

4 u + 49 = 3 u + 57
4 u - 3 u = 57 - 49

1 u = 8

Number of starfruits on his van after collecting from Mart J
= 3 u + 57
= 3 x 8 + 57
= 24 + 57
= 81

Number of fruits on his van after collecting from Mart J
= 2 x 81 
= 162 

(b)
Number of starfruits delivered to Mart H
= 18 u - 3 u
= 15 u
= 15 x 8
= 120

Answer(s): (a) 162; (b) 120