Bobby had to collect some fruits from two markets and deliver some fruits to another market. He collected from Market K and the ratio of mangosteens to starfruits was 3 : 4. When he reached Market L, he unloaded ³₄ of the starfruits and some mangosteens from his van. The ratio of mangosteens to starfruits became 3 : 4. At Market M, 29 mangosteens and 12 starfruits were collected and the number of mangosteens to starfruits became the same.

1. How many fruits were there on his van after visiting Market M?
2. How many mangosteens were delivered to Market L?

	Location	Mangosteens	Starfruits
Comparing mangosteens and starfruits at first	Market K	3x4 = 12 u	4x4 = 16 u
Before 1	Market K	12 u	4x4 = 16 u
Change 1	Market L	- ?	- 3x4 = - 12 u
After 1	Market M	3 u	1x4 = 4 u
Before 2	Market M	3x1 = 3 u	4x1 = 4 u
Change 2	Market M	+ 29	+ 12
After 2	Market M	3 u + 29	4 u + 12

(a)
The number of starfruits after unloading at Market L is repeated.  Make the number of starfruits left after unloading at Market L the same.  LCM of 4 and 1 is 4.

The number of starfruits collected at Market K is repeated.  Make the number of starfruits collected at Market K the same by multiplying 4 by 4. 
 
The number of mangosteens and starfruits in the end is the same.

4 u + 12 = 3 u + 29
4 u - 3 u = 29 - 12

1 u = 17

Number of mangosteens on his van after collecting from Market M
= 3 u + 29
= 3 x 17 + 29
= 51 + 29
= 80

Number of fruits on his van after collecting from Market M
= 2 x 80 
= 160 

(b)
Number of mangosteens delivered to Market L
= 12 u - 3 u
= 9 u
= 9 x 17
= 153

Answer(s): (a) 160; (b) 153