PSLE
Gem bought some lollipops and gave half of it to Nick. Nick bought some candy canes and gave half of it to Gem. Gem ate 6 candy canes and Nick ate 21 lollipops. The ratio of Gem's candy canes to lollipops became 1 : 6 and the ratio of Nick's candy canes to lollipops became 1 : 3. How many lollipops did Gem buy?

	Gem		Nick
	Candy canes	Lollipops	Candy canes	Lollipops
Before	1 u + 6	6 u	1 p	3 p + 21
Change	- 6			- 21
After	1 u	6 u	1 p	3 p

After Gem gave half of the lollipops to Nick and Nick gave half of his candy canes to Gem, Nick and Gem had same number of candy canes and lollipops before each ate some.

6 u = 3 p + 21 
6 u - 21 = 3 p --- (1)

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

Make p the same.

(2)_x3
3 u + 18 = 3 p --- (3)

(1) = (3)
6 u - 21 = 3 u + 18 
6 u - 3 u = 18 + 21
3 u = 39

1 u = 39 ÷ 3 = 13

Number of lollipops that Gem bought
= 2 x 6 u
= 12 u
= 12 x 13
= 156

Answer(s): 156