PSLE
Irene bought some sweets and gave half of it to Mark. Mark bought some candy canes and gave half of it to Irene. Irene ate 2 candy canes and Mark ate 56 sweets. The ratio of Irene's candy canes to sweets became 1 : 6 and the ratio of Mark's candy canes to sweets became 1 : 2. How many sweets did Irene buy?

	Irene		Mark
	Candy canes	Sweets	Candy canes	Sweets
Before	1 u + 2	6 u	1 p	2 p + 56
Change	- 2			- 56
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 56 
6 u - 56 = 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 - 56 = 2 u + 4 
6 u - 2 u = 4 + 56
4 u = 60

1 u = 60 ÷ 4 = 15

Number of sweets that Irene bought
= 2 x 6 u
= 12 u
= 12 x 15
= 180

Answer(s): 180