Cody had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall L and the ratio of pears to pomegranates was 2 : 3. When he reached Stall M, he unloaded ¹¹₁₂ of the pomegranates and some pears from his vehicle. The ratio of pears to pomegranates became 3 : 4. At Stall N, 31 pears and 11 pomegranates were collected and the number of pears to pomegranates became the same.

1. How many fruits were there on his vehicle after visiting Stall N?
2. How many pears were delivered to Stall M?

	Location	Pears	Pomegranates
Comparing pears and pomegranates at first	Stall L	2x16 = 32 u	3x16 = 48 u
Before 1	Stall L	32 u	12x4 = 48 u
Change 1	Stall M	- ?	- 11x4 = - 44 u
After 1	Stall N	3 u	1x4 = 4 u
Before 2	Stall N	3x1 = 3 u	4x1 = 4 u
Change 2	Stall N	+ 31	+ 11
After 2	Stall N	3 u + 31	4 u + 11

(a)
The number of pomegranates after unloading at Stall M is repeated.  Make the number of pomegranates left after unloading at Stall M the same.  LCM of 4 and 1 is 4.

The number of pomegranates collected at Stall L is repeated.  Make the number of pomegranates collected at Stall L the same by multiplying 3 by 16. 
 
The number of pears and pomegranates in the end is the same.

4 u + 11 = 3 u + 31
4 u - 3 u = 31 - 11

1 u = 20

Number of pears on his vehicle after collecting from Stall N
= 3 u + 31
= 3 x 20 + 31
= 60 + 31
= 91

Number of fruits on his vehicle after collecting from Stall N
= 2 x 91 
= 182 

(b)
Number of pears delivered to Stall M
= 32 u - 3 u
= 29 u
= 29 x 20
= 580

Answer(s): (a) 182; (b) 580