Rael had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket U and the ratio of persimmons to mangosteens was 7 : 10. When he reached Supermarket V, he unloaded ⁹₁₀ of the mangosteens and some persimmons from his vehicle. The ratio of persimmons to mangosteens became 1 : 2. At Supermarket W, 38 persimmons and 18 mangosteens were collected and the number of persimmons to mangosteens became the same.

1. How many fruits were there on his vehicle after visiting Supermarket W?
2. How many persimmons were delivered to Supermarket V?

	Location	Persimmons	Mangosteens
Comparing persimmons and mangosteens at first	Supermarket U	7x2 = 14 u	10x2 = 20 u
Before 1	Supermarket U	14 u	10x2 = 20 u
Change 1	Supermarket V	- ?	- 9x2 = - 18 u
After 1	Supermarket W	1 u	1x2 = 2 u
Before 2	Supermarket W	1x1 = 1 u	2x1 = 2 u
Change 2	Supermarket W	+ 38	+ 18
After 2	Supermarket W	1 u + 38	2 u + 18

(a)
The number of mangosteens after unloading at Supermarket V is repeated.  Make the number of mangosteens left after unloading at Supermarket V the same.  LCM of 2 and 1 is 2.

The number of mangosteens collected at Supermarket U is repeated.  Make the number of mangosteens collected at Supermarket U the same by multiplying 10 by 2. 
 
The number of persimmons and mangosteens in the end is the same.

2 u + 18 = 1 u + 38
2 u - 1 u = 38 - 18

1 u = 20

Number of persimmons on his vehicle after collecting from Supermarket W
= 1 u + 38
= 1 x 20 + 38
= 20 + 38
= 58

Number of fruits on his vehicle after collecting from Supermarket W
= 2 x 58 
= 116 

(b)
Number of persimmons delivered to Supermarket V
= 14 u - 1 u
= 13 u
= 13 x 20
= 260

Answer(s): (a) 116; (b) 260