PSLE
Irene bought some lollipops and gave half of it to Sam. Sam bought some chocolate bars and gave half of it to Irene. Irene ate 7 chocolate bars and Sam ate 18 lollipops. The ratio of Irene's chocolate bars to lollipops became 1 : 6 and the ratio of Sam's chocolate bars to lollipops became 1 : 2. How many lollipops did Irene buy?

	Irene		Sam
	Chocolate bars	Lollipops	Chocolate bars	Lollipops
Before	1 u + 7	6 u	1 p	2 p + 18
Change	- 7			- 18
After	1 u	6 u	1 p	2 p

After Irene gave half of the lollipops to Sam and Sam gave half of his chocolate bars to Irene, Sam and Irene had same number of chocolate bars and lollipops before each ate some.

6 u = 2 p + 18 
6 u - 18 = 2 p --- (1)

1 u + 7 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 14 = 2 p --- (3)

(1) = (3)
6 u - 18 = 2 u + 14 
6 u - 2 u = 14 + 18
4 u = 32

1 u = 32 ÷ 4 = 8

Number of lollipops that Irene bought
= 2 x 6 u
= 12 u
= 12 x 8
= 96

Answer(s): 96