Oliver had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart G and the ratio of pears to starfruits was 5 : 6. When he reached Mart H, he unloaded ¹¹₁₂ of the starfruits and some pears from his lorry. The ratio of pears to starfruits became 1 : 2. At Mart J, 34 pears and 15 starfruits were collected and the number of pears to starfruits became the same.

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

	Location	Pears	Starfruits
Comparing pears and starfruits at first	Mart G	5x4 = 20 u	6x4 = 24 u
Before 1	Mart G	20 u	12x2 = 24 u
Change 1	Mart H	- ?	- 11x2 = - 22 u
After 1	Mart J	1 u	1x2 = 2 u
Before 2	Mart J	1x1 = 1 u	2x1 = 2 u
Change 2	Mart J	+ 34	+ 15
After 2	Mart J	1 u + 34	2 u + 15

(a)
The number of starfruits after unloading at Mart H is repeated.  Make the number of starfruits left after unloading at Mart H the same.  LCM of 2 and 1 is 2.

The number of starfruits collected at Mart G is repeated.  Make the number of starfruits collected at Mart G the same by multiplying 6 by 4. 
 
The number of pears and starfruits in the end is the same.

2 u + 15 = 1 u + 34
2 u - 1 u = 34 - 15

1 u = 19

Number of pears on his lorry after collecting from Mart J
= 1 u + 34
= 1 x 19 + 34
= 19 + 34
= 53

Number of fruits on his lorry after collecting from Mart J
= 2 x 53 
= 106 

(b)
Number of pears delivered to Mart H
= 20 u - 1 u
= 19 u
= 19 x 19
= 361

Answer(s): (a) 106; (b) 361