Luke had to collect some fruits from two markets and deliver some fruits to another market. He collected from Market H and the ratio of pears to oranges was 1 : 2. When he reached Market J, he unloaded ⁵₆ of the oranges and some pears from his van. The ratio of pears to oranges became 1 : 2. At Market K, 51 pears and 36 oranges were collected and the number of pears to oranges became the same.

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

	Location	Pears	Oranges
Comparing pears and oranges at first	Market H	1x6 = 6 u	2x6 = 12 u
Before 1	Market H	6 u	6x2 = 12 u
Change 1	Market J	- ?	- 5x2 = - 10 u
After 1	Market K	1 u	1x2 = 2 u
Before 2	Market K	1x1 = 1 u	2x1 = 2 u
Change 2	Market K	+ 51	+ 36
After 2	Market K	1 u + 51	2 u + 36

(a)
The number of oranges after unloading at Market J is repeated.  Make the number of oranges left after unloading at Market J the same.  LCM of 2 and 1 is 2.

The number of oranges collected at Market H is repeated.  Make the number of oranges collected at Market H the same by multiplying 2 by 6. 
 
The number of pears and oranges in the end is the same.

2 u + 36 = 1 u + 51
2 u - 1 u = 51 - 36

1 u = 15

Number of pears on his van after collecting from Market K
= 1 u + 51
= 1 x 15 + 51
= 15 + 51
= 66

Number of fruits on his van after collecting from Market K
= 2 x 66 
= 132 

(b)
Number of pears delivered to Market J
= 6 u - 1 u
= 5 u
= 5 x 15
= 75

Answer(s): (a) 132; (b) 75