PSLE
Gwen bought some candy canes and gave half of it to Elijah. Elijah bought some chocolate bars and gave half of it to Gwen. Gwen ate 2 chocolate bars and Elijah ate 6 candy canes. The ratio of Gwen's chocolate bars to candy canes became 1 : 5 and the ratio of Elijah's chocolate bars to candy canes became 1 : 3. How many chocolate bars did Elijah buy?

	Gwen		Elijah
	Chocolate bars	Candy canes	Chocolate bars	Candy canes
Before	1 u + 2	5 u	1 p	3 p + 6
Change	- 2			- 6
After	1 u	5 u	1 p	3 p

After Gwen gave half of the candy canes to Elijah and Elijah gave half of his chocolate bars to Gwen, Elijah and Gwen had same number of chocolate bars and candy canes before each ate some.

5 u = 3 p + 6 
5 u - 6 = 3 p --- (1)

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

Make p the same.

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

(1) = (3)
5 u - 6 = 3 u + 6 
5 u - 3 u = 6 + 6
2 u = 12

1 u = 12 ÷ 2 = 6

1 p
= 1 u + 2
= 6 + 2
= 8

Number of chocolate bars that Elijah bought
= 2 p
= 2 x 8
= 16

Answer(s): 16