Jeremy had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop S and the ratio of pomegranates to oranges was 3 : 4. When he reached Shop T, he unloaded ¹¹₁₂ of the oranges and some pomegranates from his lorry. The ratio of pomegranates to oranges became 2 : 3. At Shop U, 57 pomegranates and 47 oranges were collected and the number of pomegranates to oranges became the same.

1. How many fruits were there on his lorry after visiting Shop U?
2. How many pomegranates were delivered to Shop T?

	Location	Pomegranates	Oranges
Comparing pomegranates and oranges at first	Shop S	3x9 = 27 u	4x9 = 36 u
Before 1	Shop S	27 u	12x3 = 36 u
Change 1	Shop T	- ?	- 11x3 = - 33 u
After 1	Shop U	2 u	1x3 = 3 u
Before 2	Shop U	2x1 = 2 u	3x1 = 3 u
Change 2	Shop U	+ 57	+ 47
After 2	Shop U	2 u + 57	3 u + 47

(a)
The number of oranges after unloading at Shop T is repeated.  Make the number of oranges left after unloading at Shop T the same.  LCM of 3 and 1 is 3.

The number of oranges collected at Shop S is repeated.  Make the number of oranges collected at Shop S the same by multiplying 4 by 9. 
 
The number of pomegranates and oranges in the end is the same.

3 u + 47 = 2 u + 57
3 u - 2 u = 57 - 47

1 u = 10

Number of pomegranates on his lorry after collecting from Shop U
= 2 u + 57
= 2 x 10 + 57
= 20 + 57
= 77

Number of fruits on his lorry after collecting from Shop U
= 2 x 77 
= 154 

(b)
Number of pomegranates delivered to Shop T
= 27 u - 2 u
= 25 u
= 25 x 10
= 250

Answer(s): (a) 154; (b) 250