PSLE
Jane bought some lollipops and gave half of it to Jenson. Jenson bought some sweets and gave half of it to Jane. Jane ate 6 sweets and Jenson ate 9 lollipops. The ratio of Jane's sweets to lollipops became 1 : 6 and the ratio of Jenson's sweets to lollipops became 1 : 3. How many sweets did Jenson buy?

	Jane		Jenson
	Sweets	Lollipops	Sweets	Lollipops
Before	1 u + 6	6 u	1 p	3 p + 9
Change	- 6			- 9
After	1 u	6 u	1 p	3 p

After Jane gave half of the lollipops to Jenson and Jenson gave half of his sweets to Jane, Jenson and Jane had same number of sweets and lollipops before each ate some.

6 u = 3 p + 9 
6 u - 9 = 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 - 9 = 3 u + 18 
6 u - 3 u = 18 + 9
3 u = 27

1 u = 27 ÷ 3 = 9

1 p
= 1 u + 6
= 9 + 6
= 15

Number of sweets that Jenson bought
= 2 p
= 2 x 15
= 30

Answer(s): 30