Owen had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop H and the ratio of pears to kiwis was 5 : 9. When he reached Shop J, he unloaded ⁵₆ of the kiwis and some pears from his lorry. The ratio of pears to kiwis became 2 : 3. At Shop K, 64 pears and 46 kiwis were collected and the number of pears to kiwis became the same.

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

	Location	Pears	Kiwis
Comparing pears and kiwis at first	Shop H	5x2 = 10 u	9x2 = 18 u
Before 1	Shop H	10 u	6x3 = 18 u
Change 1	Shop J	- ?	- 5x3 = - 15 u
After 1	Shop K	2 u	1x3 = 3 u
Before 2	Shop K	2x1 = 2 u	3x1 = 3 u
Change 2	Shop K	+ 64	+ 46
After 2	Shop K	2 u + 64	3 u + 46

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

The number of kiwis collected at Shop H is repeated.  Make the number of kiwis collected at Shop H the same by multiplying 9 by 2. 
 
The number of pears and kiwis in the end is the same.

3 u + 46 = 2 u + 64
3 u - 2 u = 64 - 46

1 u = 18

Number of pears on his lorry after collecting from Shop K
= 2 u + 64
= 2 x 18 + 64
= 36 + 64
= 100

Number of fruits on his lorry after collecting from Shop K
= 2 x 100 
= 200 

(b)
Number of pears delivered to Shop J
= 10 u - 2 u
= 8 u
= 8 x 18
= 144

Answer(s): (a) 200; (b) 144