Bryan had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop M and the ratio of kiwis to pomegranates was 2 : 3. When he reached Shop N, he unloaded ⁷₈ of the pomegranates and some kiwis from his lorry. The ratio of kiwis to pomegranates became 2 : 3. At Shop P, 16 kiwis and 12 pomegranates were collected and the number of kiwis to pomegranates became the same.

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

	Location	Kiwis	Pomegranates
Comparing kiwis and pomegranates at first	Shop M	2x8 = 16 u	3x8 = 24 u
Before 1	Shop M	16 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	+ 16	+ 12
After 2	Shop P	2 u + 16	3 u + 12

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

The number of pomegranates collected at Shop M is repeated.  Make the number of pomegranates collected at Shop M the same by multiplying 3 by 8. 
 
The number of kiwis and pomegranates in the end is the same.

3 u + 12 = 2 u + 16
3 u - 2 u = 16 - 12

1 u = 4

Number of kiwis on his lorry after collecting from Shop P
= 2 u + 16
= 2 x 4 + 16
= 8 + 16
= 24

Number of fruits on his lorry after collecting from Shop P
= 2 x 24 
= 48 

(b)
Number of kiwis delivered to Shop N
= 16 u - 2 u
= 14 u
= 14 x 4
= 56

Answer(s): (a) 48; (b) 56