Jenson had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop M and the ratio of pears to starfruits was 1 : 4. When he reached Shop N, he unloaded ⁷₈ of the starfruits and some pears from his van. The ratio of pears to starfruits became 2 : 3. At Shop P, 27 pears and 17 starfruits were collected and the number of pears to starfruits became the same.

1. How many fruits were there on his van after visiting Shop P?
2. How many pears were delivered to Shop N?

	Location	Pears	Starfruits
Comparing pears and starfruits at first	Shop M	1x6 = 6 u	4x6 = 24 u
Before 1	Shop M	6 u	8x3 = 24 u
Change 1	Shop N	- ?	- 7x3 = - 21 u
After 1	Shop P	2 u	1x3 = 3 u
Before 2	Shop P	2x1 = 2 u	3x1 = 3 u
Change 2	Shop P	+ 27	+ 17
After 2	Shop P	2 u + 27	3 u + 17

(a)
The number of starfruits after unloading at Shop N is repeated.  Make the number of starfruits left after unloading at Shop N the same.  LCM of 3 and 1 is 3.

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

3 u + 17 = 2 u + 27
3 u - 2 u = 27 - 17

1 u = 10

Number of pears on his van after collecting from Shop P
= 2 u + 27
= 2 x 10 + 27
= 20 + 27
= 47

Number of fruits on his van after collecting from Shop P
= 2 x 47 
= 94 

(b)
Number of pears delivered to Shop N
= 6 u - 2 u
= 4 u
= 4 x 10
= 40

Answer(s): (a) 94; (b) 40