PSLE
Xandra bought some sweets and gave half of it to Sam. Sam bought some lollipops and gave half of it to Xandra. Xandra ate 7 lollipops and Sam ate 9 sweets. The ratio of Xandra's lollipops to sweets became 1 : 6 and the ratio of Sam's lollipops to sweets became 1 : 3. How many lollipops did Sam buy?

	Xandra		Sam
	Lollipops	Sweets	Lollipops	Sweets
Before	1 u + 7	6 u	1 p	3 p + 9
Change	- 7			- 9
After	1 u	6 u	1 p	3 p

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

6 u = 3 p + 9 
6 u - 9 = 3 p --- (1)

1 u + 7 = 1 p --- (2)

Make p the same.

(2)_x3
3 u + 21 = 3 p --- (3)

(1) = (3)
6 u - 9 = 3 u + 21 
6 u - 3 u = 21 + 9
3 u = 30

1 u = 30 ÷ 3 = 10

1 p
= 1 u + 7
= 10 + 7
= 17

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

Answer(s): 34