PSLE
Lucy bought some chocolate bars and gave half of it to Sam. Sam bought some candy canes and gave half of it to Lucy. Lucy ate 3 candy canes and Sam ate 15 chocolate bars. The ratio of Lucy's candy canes to chocolate bars became 1 : 5 and the ratio of Sam's candy canes to chocolate bars became 1 : 2. How many candy canes did Sam buy?

	Lucy		Sam
	Candy canes	Chocolate bars	Candy canes	Chocolate bars
Before	1 u + 3	5 u	1 p	2 p + 15
Change	- 3			- 15
After	1 u	5 u	1 p	2 p

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

5 u = 2 p + 15 
5 u - 15 = 2 p --- (1)

1 u + 3 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 6 = 2 p --- (3)

(1) = (3)
5 u - 15 = 2 u + 6 
5 u - 2 u = 6 + 15
3 u = 21

1 u = 21 ÷ 3 = 7

1 p
= 1 u + 3
= 7 + 3
= 10

Number of candy canes that Sam bought
= 2 p
= 2 x 10
= 20

Answer(s): 20