Glen had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket M and the ratio of lemons to passion fruits was 1 : 2. When he reached Supermarket N, he unloaded ⁵₆ of the passion fruits and some lemons from his lorry. The ratio of lemons to passion fruits became 2 : 3. At Supermarket P, 33 lemons and 16 passion fruits were collected and the number of lemons to passion fruits became the same.

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

	Location	Lemons	Passion Fruits
Comparing lemons and passion fruits at first	Supermarket M	1x9 = 9 u	2x9 = 18 u
Before 1	Supermarket M	9 u	6x3 = 18 u
Change 1	Supermarket N	- ?	- 5x3 = - 15 u
After 1	Supermarket P	2 u	1x3 = 3 u
Before 2	Supermarket P	2x1 = 2 u	3x1 = 3 u
Change 2	Supermarket P	+ 33	+ 16
After 2	Supermarket P	2 u + 33	3 u + 16

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

The number of passion fruits collected at Supermarket M is repeated.  Make the number of passion fruits collected at Supermarket M the same by multiplying 2 by 9. 
 
The number of lemons and passion fruits in the end is the same.

3 u + 16 = 2 u + 33
3 u - 2 u = 33 - 16

1 u = 17

Number of lemons on his lorry after collecting from Supermarket P
= 2 u + 33
= 2 x 17 + 33
= 34 + 33
= 67

Number of fruits on his lorry after collecting from Supermarket P
= 2 x 67 
= 134 

(b)
Number of lemons delivered to Supermarket N
= 9 u - 2 u
= 7 u
= 7 x 17
= 119

Answer(s): (a) 134; (b) 119