PSLE
Barbara bought some candy canes and gave half of it to Lee. Lee bought some chocolate bars and gave half of it to Barbara. Barbara ate 5 chocolate bars and Lee ate 23 candy canes. The ratio of Barbara's chocolate bars to candy canes became 1 : 5 and the ratio of Lee's chocolate bars to candy canes became 1 : 2. How many chocolate bars did Lee buy?

	Barbara		Lee
	Chocolate bars	Candy canes	Chocolate bars	Candy canes
Before	1 u + 5	5 u	1 p	2 p + 23
Change	- 5			- 23
After	1 u	5 u	1 p	2 p

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

5 u = 2 p + 23 
5 u - 23 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 10 = 2 p --- (3)

(1) = (3)
5 u - 23 = 2 u + 10 
5 u - 2 u = 10 + 23
3 u = 33

1 u = 33 ÷ 3 = 11

1 p
= 1 u + 5
= 11 + 5
= 16

Number of chocolate bars that Lee bought
= 2 p
= 2 x 16
= 32

Answer(s): 32