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 mangoes to starfruits was 5 : 6. When he reached Supermarket Q, he unloaded ⁵₆ of the starfruits and some mangoes from his vehicle. The ratio of mangoes to starfruits became 2 : 3. At Supermarket R, 28 mangoes and 11 starfruits were collected and the number of mangoes to starfruits became the same.

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

	Location	Mangoes	Starfruits
Comparing mangoes and starfruits at first	Supermarket P	5x3 = 15 u	6x3 = 18 u
Before 1	Supermarket P	15 u	6x3 = 18 u
Change 1	Supermarket Q	- ?	- 5x3 = - 15 u
After 1	Supermarket R	2 u	1x3 = 3 u
Before 2	Supermarket R	2x1 = 2 u	3x1 = 3 u
Change 2	Supermarket R	+ 28	+ 11
After 2	Supermarket R	2 u + 28	3 u + 11

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

The number of starfruits collected at Supermarket P is repeated.  Make the number of starfruits collected at Supermarket P the same by multiplying 6 by 3. 
 
The number of mangoes and starfruits in the end is the same.

3 u + 11 = 2 u + 28
3 u - 2 u = 28 - 11

1 u = 17

Number of mangoes on his vehicle after collecting from Supermarket R
= 2 u + 28
= 2 x 17 + 28
= 34 + 28
= 62

Number of fruits on his vehicle after collecting from Supermarket R
= 2 x 62 
= 124 

(b)
Number of mangoes delivered to Supermarket Q
= 15 u - 2 u
= 13 u
= 13 x 17
= 221

Answer(s): (a) 124; (b) 221