Paul had to collect some fruits from two marts and deliver some fruits to another mart. He collected from Mart M and the ratio of starfruits to pears was 5 : 8. When he reached Mart N, he unloaded ¹¹₁₂ of the pears and some starfruits from his lorry. The ratio of starfruits to pears became 1 : 2. At Mart P, 23 starfruits and 20 pears were collected and the number of starfruits to pears became the same.

1. How many fruits were there on his lorry after visiting Mart P?
2. How many starfruits were delivered to Mart N?

	Location	Starfruits	Pears
Comparing starfruits and pears at first	Mart M	5x3 = 15 u	8x3 = 24 u
Before 1	Mart M	15 u	12x2 = 24 u
Change 1	Mart N	- ?	- 11x2 = - 22 u
After 1	Mart P	1 u	1x2 = 2 u
Before 2	Mart P	1x1 = 1 u	2x1 = 2 u
Change 2	Mart P	+ 23	+ 20
After 2	Mart P	1 u + 23	2 u + 20

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

The number of pears collected at Mart M is repeated.  Make the number of pears collected at Mart M the same by multiplying 8 by 3. 
 
The number of starfruits and pears in the end is the same.

2 u + 20 = 1 u + 23
2 u - 1 u = 23 - 20

1 u = 3

Number of starfruits on his lorry after collecting from Mart P
= 1 u + 23
= 1 x 3 + 23
= 3 + 23
= 26

Number of fruits on his lorry after collecting from Mart P
= 2 x 26 
= 52 

(b)
Number of starfruits delivered to Mart N
= 15 u - 1 u
= 14 u
= 14 x 3
= 42

Answer(s): (a) 52; (b) 42