PSLE
Dana bought some candy canes and gave half of it to Rael. Rael bought some lollipops and gave half of it to Dana. Dana ate 2 lollipops and Rael ate 21 candy canes. The ratio of Dana's lollipops to candy canes became 1 : 6 and the ratio of Rael's lollipops to candy canes became 1 : 3. How many lollipops did Rael buy?

	Dana		Rael
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 2	6 u	1 p	3 p + 21
Change	- 2			- 21
After	1 u	6 u	1 p	3 p

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

6 u = 3 p + 21 
6 u - 21 = 3 p --- (1)

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

Make p the same.

(2)_x3
3 u + 6 = 3 p --- (3)

(1) = (3)
6 u - 21 = 3 u + 6 
6 u - 3 u = 6 + 21
3 u = 27

1 u = 27 ÷ 3 = 9

1 p
= 1 u + 2
= 9 + 2
= 11

Number of lollipops that Rael bought
= 2 p
= 2 x 11
= 22

Answer(s): 22