Ryan had to collect some fruits from two markets and deliver some fruits to another market. He collected from Market Q and the ratio of pomegranates to passion fruits was 7 : 8. When he reached Market R, he unloaded ⁵₆ of the passion fruits and some pomegranates from his lorry. The ratio of pomegranates to passion fruits became 3 : 4. At Market S, 48 pomegranates and 30 passion fruits were collected and the number of pomegranates to passion fruits became the same.

1. How many fruits were there on his lorry after visiting Market S?
2. How many pomegranates were delivered to Market R?

	Location	Pomegranates	Passion Fruits
Comparing pomegranates and passion fruits at first	Market Q	7x3 = 21 u	8x3 = 24 u
Before 1	Market Q	21 u	6x4 = 24 u
Change 1	Market R	- ?	- 5x4 = - 20 u
After 1	Market S	3 u	1x4 = 4 u
Before 2	Market S	3x1 = 3 u	4x1 = 4 u
Change 2	Market S	+ 48	+ 30
After 2	Market S	3 u + 48	4 u + 30

(a)
The number of passion fruits after unloading at Market R is repeated.  Make the number of passion fruits left after unloading at Market R the same.  LCM of 4 and 1 is 4.

The number of passion fruits collected at Market Q is repeated.  Make the number of passion fruits collected at Market Q the same by multiplying 8 by 3. 
 
The number of pomegranates and passion fruits in the end is the same.

4 u + 30 = 3 u + 48
4 u - 3 u = 48 - 30

1 u = 18

Number of pomegranates on his lorry after collecting from Market S
= 3 u + 48
= 3 x 18 + 48
= 54 + 48
= 102

Number of fruits on his lorry after collecting from Market S
= 2 x 102 
= 204 

(b)
Number of pomegranates delivered to Market R
= 21 u - 3 u
= 18 u
= 18 x 18
= 324

Answer(s): (a) 204; (b) 324