Tim had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket X and the ratio of kiwis to pomegranates was 5 : 8. When he reached Supermarket Y, he unloaded ⁷₈ of the pomegranates and some kiwis from his vehicle. The ratio of kiwis to pomegranates became 1 : 2. At Supermarket Z, 59 kiwis and 42 pomegranates were collected and the number of kiwis to pomegranates became the same.

1. How many fruits were there on his vehicle after visiting Supermarket Z?
2. How many kiwis were delivered to Supermarket Y?

	Location	Kiwis	Pomegranates
Comparing kiwis and pomegranates at first	Supermarket X	5x2 = 10 u	8x2 = 16 u
Before 1	Supermarket X	10 u	8x2 = 16 u
Change 1	Supermarket Y	- ?	- 7x2 = - 14 u
After 1	Supermarket Z	1 u	1x2 = 2 u
Before 2	Supermarket Z	1x1 = 1 u	2x1 = 2 u
Change 2	Supermarket Z	+ 59	+ 42
After 2	Supermarket Z	1 u + 59	2 u + 42

(a)
The number of pomegranates after unloading at Supermarket Y is repeated.  Make the number of pomegranates left after unloading at Supermarket Y the same.  LCM of 2 and 1 is 2.

The number of pomegranates collected at Supermarket X is repeated.  Make the number of pomegranates collected at Supermarket X the same by multiplying 8 by 2. 
 
The number of kiwis and pomegranates in the end is the same.

2 u + 42 = 1 u + 59
2 u - 1 u = 59 - 42

1 u = 17

Number of kiwis on his vehicle after collecting from Supermarket Z
= 1 u + 59
= 1 x 17 + 59
= 17 + 59
= 76

Number of fruits on his vehicle after collecting from Supermarket Z
= 2 x 76 
= 152 

(b)
Number of kiwis delivered to Supermarket Y
= 10 u - 1 u
= 9 u
= 9 x 17
= 153

Answer(s): (a) 152; (b) 153