Ivan had to collect some fruits from two markets and deliver some fruits to another market. He collected from Market J and the ratio of pears to pomegranates was 3 : 4. When he reached Market K, he unloaded ⁷₈ of the pomegranates and some pears from his van. The ratio of pears to pomegranates became 2 : 3. At Market L, 55 pears and 38 pomegranates were collected and the number of pears to pomegranates became the same.

1. How many fruits were there on his van after visiting Market L?
2. How many pears were delivered to Market K?

	Location	Pears	Pomegranates
Comparing pears and pomegranates at first	Market J	3x6 = 18 u	4x6 = 24 u
Before 1	Market J	18 u	8x3 = 24 u
Change 1	Market K	- ?	- 7x3 = - 21 u
After 1	Market L	2 u	1x3 = 3 u
Before 2	Market L	2x1 = 2 u	3x1 = 3 u
Change 2	Market L	+ 55	+ 38
After 2	Market L	2 u + 55	3 u + 38

(a)
The number of pomegranates after unloading at Market K is repeated.  Make the number of pomegranates left after unloading at Market K the same.  LCM of 3 and 1 is 3.

The number of pomegranates collected at Market J is repeated.  Make the number of pomegranates collected at Market J the same by multiplying 4 by 6. 
 
The number of pears and pomegranates in the end is the same.

3 u + 38 = 2 u + 55
3 u - 2 u = 55 - 38

1 u = 17

Number of pears on his van after collecting from Market L
= 2 u + 55
= 2 x 17 + 55
= 34 + 55
= 89

Number of fruits on his van after collecting from Market L
= 2 x 89 
= 178 

(b)
Number of pears delivered to Market K
= 18 u - 2 u
= 16 u
= 16 x 17
= 272

Answer(s): (a) 178; (b) 272