PSLE
Xuan bought some candy canes and gave half of it to George. George bought some lollipops and gave half of it to Xuan. Xuan ate 3 lollipops and George ate 54 candy canes. The ratio of Xuan's lollipops to candy canes became 1 : 6 and the ratio of George's lollipops to candy canes became 1 : 2. How many lollipops did George buy?

	Xuan		George
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 3	6 u	1 p	2 p + 54
Change	- 3			- 54
After	1 u	6 u	1 p	2 p

After Xuan gave half of the candy canes to George and George gave half of his lollipops to Xuan, George and Xuan had same number of lollipops and candy canes before each ate some.

6 u = 2 p + 54 
6 u - 54 = 2 p --- (1)

1 u + 3 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 6 = 2 p --- (3)

(1) = (3)
6 u - 54 = 2 u + 6 
6 u - 2 u = 6 + 54
4 u = 60

1 u = 60 ÷ 4 = 15

1 p
= 1 u + 3
= 15 + 3
= 18

Number of lollipops that George bought
= 2 p
= 2 x 18
= 36

Answer(s): 36