PSLE
Victoria bought some candy canes and gave half of it to Zane. Zane bought some lollipops and gave half of it to Victoria. Victoria ate 10 lollipops and Zane ate 16 candy canes. The ratio of Victoria's lollipops to candy canes became 1 : 6 and the ratio of Zane's lollipops to candy canes became 1 : 2. How many lollipops did Zane buy?

	Victoria		Zane
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 10	6 u	1 p	2 p + 16
Change	- 10			- 16
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 16 
6 u - 16 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 20 = 2 p --- (3)

(1) = (3)
6 u - 16 = 2 u + 20 
6 u - 2 u = 20 + 16
4 u = 36

1 u = 36 ÷ 4 = 9

1 p
= 1 u + 10
= 9 + 10
= 19

Number of lollipops that Zane bought
= 2 p
= 2 x 19
= 38

Answer(s): 38