PSLE
Elyse bought some lollipops and gave half of it to Ben. Ben bought some candy canes and gave half of it to Elyse. Elyse ate 9 candy canes and Ben ate 2 lollipops. The ratio of Elyse's candy canes to lollipops became 1 : 6 and the ratio of Ben's candy canes to lollipops became 1 : 2. How many candy canes did Ben buy?

	Elyse		Ben
	Candy canes	Lollipops	Candy canes	Lollipops
Before	1 u + 9	6 u	1 p	2 p + 2
Change	- 9			- 2
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 2 
6 u - 2 = 2 p --- (1)

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

Make p the same.

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

(1) = (3)
6 u - 2 = 2 u + 18 
6 u - 2 u = 18 + 2
4 u = 20

1 u = 20 ÷ 4 = 5

1 p
= 1 u + 9
= 5 + 9
= 14

Number of candy canes that Ben bought
= 2 p
= 2 x 14
= 28

Answer(s): 28