PSLE
Olivia bought some jelly beans and gave half of it to Charlie. Charlie bought some candy canes and gave half of it to Olivia. Olivia ate 2 candy canes and Charlie ate 8 jelly beans. The ratio of Olivia's candy canes to jelly beans became 1 : 5 and the ratio of Charlie's candy canes to jelly beans became 1 : 2. How many jelly beans did Olivia buy?

	Olivia		Charlie
	Candy canes	Jelly beans	Candy canes	Jelly beans
Before	1 u + 2	5 u	1 p	2 p + 8
Change	- 2			- 8
After	1 u	5 u	1 p	2 p

After Olivia gave half of the jelly beans to Charlie and Charlie gave half of his candy canes to Olivia, Charlie and Olivia had same number of candy canes and jelly beans before each ate some.

5 u = 2 p + 8 
5 u - 8 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 4 = 2 p --- (3)

(1) = (3)
5 u - 8 = 2 u + 4 
5 u - 2 u = 4 + 8
3 u = 12

1 u = 12 ÷ 3 = 4

Number of jelly beans that Olivia bought
= 2 x 5 u
= 10 u
= 10 x 4
= 40

Answer(s): 40