PSLE
Diana bought some candy canes and gave half of it to Charlie. Charlie bought some chocolate bars and gave half of it to Diana. Diana ate 3 chocolate bars and Charlie ate 21 candy canes. The ratio of Diana's chocolate bars to candy canes became 1 : 6 and the ratio of Charlie's chocolate bars to candy canes became 1 : 3. How many chocolate bars did Charlie buy?

	Diana		Charlie
	Chocolate bars	Candy canes	Chocolate bars	Candy canes
Before	1 u + 3	6 u	1 p	3 p + 21
Change	- 3			- 21
After	1 u	6 u	1 p	3 p

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

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

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

Make p the same.

(2)_x3
3 u + 9 = 3 p --- (3)

(1) = (3)
6 u - 21 = 3 u + 9 
6 u - 3 u = 9 + 21
3 u = 30

1 u = 30 ÷ 3 = 10

1 p
= 1 u + 3
= 10 + 3
= 13

Number of chocolate bars that Charlie bought
= 2 p
= 2 x 13
= 26

Answer(s): 26