PSLE
Victoria bought some lollipops and gave half of it to David. David bought some sweets and gave half of it to Victoria. Victoria ate 4 sweets and David ate 6 lollipops. The ratio of Victoria's sweets to lollipops became 1 : 6 and the ratio of David's sweets to lollipops became 1 : 4. How many sweets did David buy?

	Victoria		David
	Sweets	Lollipops	Sweets	Lollipops
Before	1 u + 4	6 u	1 p	4 p + 6
Change	- 4			- 6
After	1 u	6 u	1 p	4 p

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

6 u = 4 p + 6 
6 u - 6 = 4 p --- (1)

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

Make p the same.

(2)_x4
4 u + 16 = 4 p --- (3)

(1) = (3)
6 u - 6 = 4 u + 16 
6 u - 4 u = 16 + 6
2 u = 22

1 u = 22 ÷ 2 = 11

1 p
= 1 u + 4
= 11 + 4
= 15

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

Answer(s): 30