Cole had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop J and the ratio of starfruits to apples was 1 : 9. When he reached Shop K, he unloaded ¹¹₁₂ of the apples and some starfruits from his van. The ratio of starfruits to apples became 2 : 3. At Shop L, 44 starfruits and 31 apples were collected and the number of starfruits to apples became the same.

1. How many fruits were there on his van after visiting Shop L?
2. How many starfruits were delivered to Shop K?

	Location	Starfruits	Apples
Comparing starfruits and apples at first	Shop J	1x4 = 4 u	9x4 = 36 u
Before 1	Shop J	4 u	12x3 = 36 u
Change 1	Shop K	- ?	- 11x3 = - 33 u
After 1	Shop L	2 u	1x3 = 3 u
Before 2	Shop L	2x1 = 2 u	3x1 = 3 u
Change 2	Shop L	+ 44	+ 31
After 2	Shop L	2 u + 44	3 u + 31

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

The number of apples collected at Shop J is repeated.  Make the number of apples collected at Shop J the same by multiplying 9 by 4. 
 
The number of starfruits and apples in the end is the same.

3 u + 31 = 2 u + 44
3 u - 2 u = 44 - 31

1 u = 13

Number of starfruits on his van after collecting from Shop L
= 2 u + 44
= 2 x 13 + 44
= 26 + 44
= 70

Number of fruits on his van after collecting from Shop L
= 2 x 70 
= 140 

(b)
Number of starfruits delivered to Shop K
= 4 u - 2 u
= 2 u
= 2 x 13
= 26

Answer(s): (a) 140; (b) 26