PSLE
Emily bought some candy canes and gave half of it to David. David bought some lollipops and gave half of it to Emily. Emily ate 9 lollipops and David ate 9 candy canes. The ratio of Emily's lollipops to candy canes became 1 : 5 and the ratio of David's lollipops to candy canes became 1 : 2. How many lollipops did David buy?

	Emily		David
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 9	5 u	1 p	2 p + 9
Change	- 9			- 9
After	1 u	5 u	1 p	2 p

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

5 u = 2 p + 9 
5 u - 9 = 2 p --- (1)

1 u + 9 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 18 = 2 p --- (3)

(1) = (3)
5 u - 9 = 2 u + 18 
5 u - 2 u = 18 + 9
3 u = 27

1 u = 27 ÷ 3 = 9

1 p
= 1 u + 9
= 9 + 9
= 18

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

Answer(s): 36