Will had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop W and the ratio of kiwis to starfruits was 1 : 3. When he reached Shop X, he unloaded ⁵₆ of the starfruits and some kiwis from his lorry. The ratio of kiwis to starfruits became 1 : 2. At Shop Y, 35 kiwis and 30 starfruits were collected and the number of kiwis to starfruits became the same.

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

	Location	Kiwis	Starfruits
Comparing kiwis and starfruits at first	Shop W	1x4 = 4 u	3x4 = 12 u
Before 1	Shop W	4 u	6x2 = 12 u
Change 1	Shop X	- ?	- 5x2 = - 10 u
After 1	Shop Y	1 u	1x2 = 2 u
Before 2	Shop Y	1x1 = 1 u	2x1 = 2 u
Change 2	Shop Y	+ 35	+ 30
After 2	Shop Y	1 u + 35	2 u + 30

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

The number of starfruits collected at Shop W is repeated.  Make the number of starfruits collected at Shop W the same by multiplying 3 by 4. 
 
The number of kiwis and starfruits in the end is the same.

2 u + 30 = 1 u + 35
2 u - 1 u = 35 - 30

1 u = 5

Number of kiwis on his lorry after collecting from Shop Y
= 1 u + 35
= 1 x 5 + 35
= 5 + 35
= 40

Number of fruits on his lorry after collecting from Shop Y
= 2 x 40 
= 80 

(b)
Number of kiwis delivered to Shop X
= 4 u - 1 u
= 3 u
= 3 x 5
= 15

Answer(s): (a) 80; (b) 15