PSLE
Mary bought some candy canes and gave half of it to Bobby. Bobby bought some sweets and gave half of it to Mary. Mary ate 2 sweets and Bobby ate 12 candy canes. The ratio of Mary's sweets to candy canes became 1 : 6 and the ratio of Bobby's sweets to candy canes became 1 : 2. How many sweets did Bobby buy?

	Mary		Bobby
	Sweets	Candy canes	Sweets	Candy canes
Before	1 u + 2	6 u	1 p	2 p + 12
Change	- 2			- 12
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 12 
6 u - 12 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 4 = 2 p --- (3)

(1) = (3)
6 u - 12 = 2 u + 4 
6 u - 2 u = 4 + 12
4 u = 16

1 u = 16 ÷ 4 = 4

1 p
= 1 u + 2
= 4 + 2
= 6

Number of sweets that Bobby bought
= 2 p
= 2 x 6
= 12

Answer(s): 12