PSLE
Risa bought some lollipops and gave half of it to Neave. Neave bought some sweets and gave half of it to Risa. Risa ate 5 sweets and Neave ate 38 lollipops. The ratio of Risa's sweets to lollipops became 1 : 6 and the ratio of Neave's sweets to lollipops became 1 : 2. How many lollipops did Risa buy?

	Risa		Neave
	Sweets	Lollipops	Sweets	Lollipops
Before	1 u + 5	6 u	1 p	2 p + 38
Change	- 5			- 38
After	1 u	6 u	1 p	2 p

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

6 u = 2 p + 38 
6 u - 38 = 2 p --- (1)

1 u + 5 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 10 = 2 p --- (3)

(1) = (3)
6 u - 38 = 2 u + 10 
6 u - 2 u = 10 + 38
4 u = 48

1 u = 48 ÷ 4 = 12

Number of lollipops that Risa bought
= 2 x 6 u
= 12 u
= 12 x 12
= 144

Answer(s): 144