Jeremy had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop X and the ratio of mangosteens to pears was 1 : 2. When he reached Shop Y, he unloaded ⁷₈ of the pears and some mangosteens from his van. The ratio of mangosteens to pears became 3 : 4. At Shop Z, 47 mangosteens and 32 pears were collected and the number of mangosteens to pears became the same.

1. How many fruits were there on his van after visiting Shop Z?
2. How many mangosteens were delivered to Shop Y?

	Location	Mangosteens	Pears
Comparing mangosteens and pears at first	Shop X	1x16 = 16 u	2x16 = 32 u
Before 1	Shop X	16 u	8x4 = 32 u
Change 1	Shop Y	- ?	- 7x4 = - 28 u
After 1	Shop Z	3 u	1x4 = 4 u
Before 2	Shop Z	3x1 = 3 u	4x1 = 4 u
Change 2	Shop Z	+ 47	+ 32
After 2	Shop Z	3 u + 47	4 u + 32

(a)
The number of pears after unloading at Shop Y is repeated.  Make the number of pears left after unloading at Shop Y the same.  LCM of 4 and 1 is 4.

The number of pears collected at Shop X is repeated.  Make the number of pears collected at Shop X the same by multiplying 2 by 16. 
 
The number of mangosteens and pears in the end is the same.

4 u + 32 = 3 u + 47
4 u - 3 u = 47 - 32

1 u = 15

Number of mangosteens on his van after collecting from Shop Z
= 3 u + 47
= 3 x 15 + 47
= 45 + 47
= 92

Number of fruits on his van after collecting from Shop Z
= 2 x 92 
= 184 

(b)
Number of mangosteens delivered to Shop Y
= 16 u - 3 u
= 13 u
= 13 x 15
= 195

Answer(s): (a) 184; (b) 195