PSLE
Xuan bought some candy canes and gave half of it to Warren. Warren bought some lollipops and gave half of it to Xuan. Xuan ate 2 lollipops and Warren ate 10 candy canes. The ratio of Xuan's lollipops to candy canes became 1 : 4 and the ratio of Warren's lollipops to candy canes became 1 : 2. How many candy canes did Xuan buy?

	Xuan		Warren
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 2	4 u	1 p	2 p + 10
Change	- 2			- 10
After	1 u	4 u	1 p	2 p

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

4 u = 2 p + 10 
4 u - 10 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 4 = 2 p --- (3)

(1) = (3)
4 u - 10 = 2 u + 4 
4 u - 2 u = 4 + 10
2 u = 14

1 u = 14 ÷ 2 = 7

Number of candy canes that Xuan bought
= 2 x 4 u
= 8 u
= 8 x 7
= 56

Answer(s): 56