PSLE
Vanessa bought some jelly beans and gave half of it to John. John bought some candy canes and gave half of it to Vanessa. Vanessa ate 8 candy canes and John ate 6 jelly beans. The ratio of Vanessa's candy canes to jelly beans became 1 : 4 and the ratio of John's candy canes to jelly beans became 1 : 2. How many candy canes did John buy?

	Vanessa		John
	Candy canes	Jelly beans	Candy canes	Jelly beans
Before	1 u + 8	4 u	1 p	2 p + 6
Change	- 8			- 6
After	1 u	4 u	1 p	2 p

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

4 u = 2 p + 6 
4 u - 6 = 2 p --- (1)

1 u + 8 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 16 = 2 p --- (3)

(1) = (3)
4 u - 6 = 2 u + 16 
4 u - 2 u = 16 + 6
2 u = 22

1 u = 22 ÷ 2 = 11

1 p
= 1 u + 8
= 11 + 8
= 19

Number of candy canes that John bought
= 2 p
= 2 x 19
= 38

Answer(s): 38