Dylan had to collect some fruits from two stalls and deliver some fruits to another stall. He collected from Stall V and the ratio of mangoes to lemons was 3 : 4. When he reached Stall W, he unloaded ⁷₈ of the lemons and some mangoes from his vehicle. The ratio of mangoes to lemons became 2 : 3. At Stall X, 53 mangoes and 50 lemons were collected and the number of mangoes to lemons became the same.

1. How many fruits were there on his vehicle after visiting Stall X?
2. How many mangoes were delivered to Stall W?

	Location	Mangoes	Lemons
Comparing mangoes and lemons at first	Stall V	3x6 = 18 u	4x6 = 24 u
Before 1	Stall V	18 u	8x3 = 24 u
Change 1	Stall W	- ?	- 7x3 = - 21 u
After 1	Stall X	2 u	1x3 = 3 u
Before 2	Stall X	2x1 = 2 u	3x1 = 3 u
Change 2	Stall X	+ 53	+ 50
After 2	Stall X	2 u + 53	3 u + 50

(a)
The number of lemons after unloading at Stall W is repeated.  Make the number of lemons left after unloading at Stall W the same.  LCM of 3 and 1 is 3.

The number of lemons collected at Stall V is repeated.  Make the number of lemons collected at Stall V the same by multiplying 4 by 6. 
 
The number of mangoes and lemons in the end is the same.

3 u + 50 = 2 u + 53
3 u - 2 u = 53 - 50

1 u = 3

Number of mangoes on his vehicle after collecting from Stall X
= 2 u + 53
= 2 x 3 + 53
= 6 + 53
= 59

Number of fruits on his vehicle after collecting from Stall X
= 2 x 59 
= 118 

(b)
Number of mangoes delivered to Stall W
= 18 u - 2 u
= 16 u
= 16 x 3
= 48

Answer(s): (a) 118; (b) 48