PSLE
Xylia bought some candy canes and gave half of it to Howard. Howard bought some sweets and gave half of it to Xylia. Xylia ate 2 sweets and Howard ate 30 candy canes. The ratio of Xylia's sweets to candy canes became 1 : 6 and the ratio of Howard's sweets to candy canes became 1 : 3. How many sweets did Howard buy?

	Xylia		Howard
	Sweets	Candy canes	Sweets	Candy canes
Before	1 u + 2	6 u	1 p	3 p + 30
Change	- 2			- 30
After	1 u	6 u	1 p	3 p

After Xylia gave half of the candy canes to Howard and Howard gave half of his sweets to Xylia, Howard and Xylia had same number of sweets and candy canes before each ate some.

6 u = 3 p + 30 
6 u - 30 = 3 p --- (1)

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

Make p the same.

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

(1) = (3)
6 u - 30 = 3 u + 6 
6 u - 3 u = 6 + 30
3 u = 36

1 u = 36 ÷ 3 = 12

1 p
= 1 u + 2
= 12 + 2
= 14

Number of sweets that Howard bought
= 2 p
= 2 x 14
= 28

Answer(s): 28