Ryan had to collect some fruits from two supermarkets and deliver some fruits to another supermarket. He collected from Supermarket P and the ratio of starfruits to mangoes was 2 : 9. When he reached Supermarket Q, he unloaded ¹¹₁₂ of the mangoes and some starfruits from his lorry. The ratio of starfruits to mangoes became 2 : 3. At Supermarket R, 30 starfruits and 16 mangoes were collected and the number of starfruits to mangoes became the same.

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

	Location	Starfruits	Mangoes
Comparing starfruits and mangoes at first	Supermarket P	2x4 = 8 u	9x4 = 36 u
Before 1	Supermarket P	8 u	12x3 = 36 u
Change 1	Supermarket Q	- ?	- 11x3 = - 33 u
After 1	Supermarket R	2 u	1x3 = 3 u
Before 2	Supermarket R	2x1 = 2 u	3x1 = 3 u
Change 2	Supermarket R	+ 30	+ 16
After 2	Supermarket R	2 u + 30	3 u + 16

(a)
The number of mangoes after unloading at Supermarket Q is repeated.  Make the number of mangoes left after unloading at Supermarket Q the same.  LCM of 3 and 1 is 3.

The number of mangoes collected at Supermarket P is repeated.  Make the number of mangoes collected at Supermarket P the same by multiplying 9 by 4. 
 
The number of starfruits and mangoes in the end is the same.

3 u + 16 = 2 u + 30
3 u - 2 u = 30 - 16

1 u = 14

Number of starfruits on his lorry after collecting from Supermarket R
= 2 u + 30
= 2 x 14 + 30
= 28 + 30
= 58

Number of fruits on his lorry after collecting from Supermarket R
= 2 x 58 
= 116 

(b)
Number of starfruits delivered to Supermarket Q
= 8 u - 2 u
= 6 u
= 6 x 14
= 84

Answer(s): (a) 116; (b) 84