PSLE
Gem bought some chocolate bars and gave half of it to Vincent. Vincent bought some lollipops and gave half of it to Gem. Gem ate 6 lollipops and Vincent ate 14 chocolate bars. The ratio of Gem's lollipops to chocolate bars became 1 : 4 and the ratio of Vincent's lollipops to chocolate bars became 1 : 2. How many lollipops did Vincent buy?

	Gem		Vincent
	Lollipops	Chocolate bars	Lollipops	Chocolate bars
Before	1 u + 6	4 u	1 p	2 p + 14
Change	- 6			- 14
After	1 u	4 u	1 p	2 p

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

4 u = 2 p + 14 
4 u - 14 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 12 = 2 p --- (3)

(1) = (3)
4 u - 14 = 2 u + 12 
4 u - 2 u = 12 + 14
2 u = 26

1 u = 26 ÷ 2 = 13

1 p
= 1 u + 6
= 13 + 6
= 19

Number of lollipops that Vincent bought
= 2 p
= 2 x 19
= 38

Answer(s): 38