Jack had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket D and the ratio of persimmons to starfruits was 7 : 8. When he reached Supermarket E, he unloaded ⁷₈ of the starfruits and some persimmons from his vehicle. The ratio of persimmons to starfruits became 1 : 2. At Supermarket F, 30 persimmons and 11 starfruits were collected and the number of persimmons to starfruits became the same.

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

	Location	Persimmons	Starfruits
Comparing persimmons and starfruits at first	Supermarket D	7x2 = 14 u	8x2 = 16 u
Before 1	Supermarket D	14 u	8x2 = 16 u
Change 1	Supermarket E	- ?	- 7x2 = - 14 u
After 1	Supermarket F	1 u	1x2 = 2 u
Before 2	Supermarket F	1x1 = 1 u	2x1 = 2 u
Change 2	Supermarket F	+ 30	+ 11
After 2	Supermarket F	1 u + 30	2 u + 11

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

The number of starfruits collected at Supermarket D is repeated.  Make the number of starfruits collected at Supermarket D the same by multiplying 8 by 2. 
 
The number of persimmons and starfruits in the end is the same.

2 u + 11 = 1 u + 30
2 u - 1 u = 30 - 11

1 u = 19

Number of persimmons on his vehicle after collecting from Supermarket F
= 1 u + 30
= 1 x 19 + 30
= 19 + 30
= 49

Number of fruits on his vehicle after collecting from Supermarket F
= 2 x 49 
= 98 

(b)
Number of persimmons delivered to Supermarket E
= 14 u - 1 u
= 13 u
= 13 x 19
= 247

Answer(s): (a) 98; (b) 247