PSLE
Nicole bought some chocolate bars and gave half of it to Ken. Ken bought some lollipops and gave half of it to Nicole. Nicole ate 3 lollipops and Ken ate 50 chocolate bars. The ratio of Nicole's lollipops to chocolate bars became 1 : 6 and the ratio of Ken's lollipops to chocolate bars became 1 : 2. How many lollipops did Ken buy?

	Nicole		Ken
	Lollipops	Chocolate bars	Lollipops	Chocolate bars
Before	1 u + 3	6 u	1 p	2 p + 50
Change	- 3			- 50
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 50 
6 u - 50 = 2 p --- (1)

1 u + 3 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 6 = 2 p --- (3)

(1) = (3)
6 u - 50 = 2 u + 6 
6 u - 2 u = 6 + 50
4 u = 56

1 u = 56 ÷ 4 = 14

1 p
= 1 u + 3
= 14 + 3
= 17

Number of lollipops that Ken bought
= 2 p
= 2 x 17
= 34

Answer(s): 34