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

	Kathy		Gabriel
	Jelly beans	Lollipops	Jelly beans	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 Kathy gave half of the lollipops to Gabriel and Gabriel gave half of his jelly beans to Kathy, Gabriel and Kathy had same number of jelly beans 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 Kathy bought
= 2 x 6 u
= 12 u
= 12 x 12
= 144

Answer(s): 144