Howard had to collect some fruits from two shops and deliver some fruits to another shop. He collected from Shop N and the ratio of starfruits to oranges was 1 : 2. When he reached Shop P, he unloaded ⁹₁₀ of the oranges and some starfruits from his lorry. The ratio of starfruits to oranges became 2 : 3. At Shop Q, 57 starfruits and 47 oranges were collected and the number of starfruits to oranges became the same.

1. How many fruits were there on his lorry after visiting Shop Q?
2. How many starfruits were delivered to Shop P?

	Location	Starfruits	Oranges
Comparing starfruits and oranges at first	Shop N	1x15 = 15 u	2x15 = 30 u
Before 1	Shop N	15 u	10x3 = 30 u
Change 1	Shop P	- ?	- 9x3 = - 27 u
After 1	Shop Q	2 u	1x3 = 3 u
Before 2	Shop Q	2x1 = 2 u	3x1 = 3 u
Change 2	Shop Q	+ 57	+ 47
After 2	Shop Q	2 u + 57	3 u + 47

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

The number of oranges collected at Shop N is repeated.  Make the number of oranges collected at Shop N the same by multiplying 2 by 15. 
 
The number of starfruits 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 starfruits on his lorry after collecting from Shop Q
= 2 u + 57
= 2 x 10 + 57
= 20 + 57
= 77

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

(b)
Number of starfruits delivered to Shop P
= 15 u - 2 u
= 13 u
= 13 x 10
= 130

Answer(s): (a) 154; (b) 130