PSLE
Usha bought some jelly beans and gave half of it to Perry. Perry bought some sweets and gave half of it to Usha. Usha ate 5 sweets and Perry ate 30 jelly beans. The ratio of Usha's sweets to jelly beans became 1 : 6 and the ratio of Perry's sweets to jelly beans became 1 : 3. How many sweets did Perry buy?

	Usha		Perry
	Sweets	Jelly beans	Sweets	Jelly beans
Before	1 u + 5	6 u	1 p	3 p + 30
Change	- 5			- 30
After	1 u	6 u	1 p	3 p

After Usha gave half of the jelly beans to Perry and Perry gave half of his sweets to Usha, Perry and Usha had same number of sweets and jelly beans before each ate some.

6 u = 3 p + 30 
6 u - 30 = 3 p --- (1)

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

Make p the same.

(2)_x3
3 u + 15 = 3 p --- (3)

(1) = (3)
6 u - 30 = 3 u + 15 
6 u - 3 u = 15 + 30
3 u = 45

1 u = 45 ÷ 3 = 15

1 p
= 1 u + 5
= 15 + 5
= 20

Number of sweets that Perry bought
= 2 p
= 2 x 20
= 40

Answer(s): 40