PSLE
Hilda bought some jelly beans and gave half of it to Simon. Simon bought some candy canes and gave half of it to Hilda. Hilda ate 4 candy canes and Simon ate 33 jelly beans. The ratio of Hilda's candy canes to jelly beans became 1 : 6 and the ratio of Simon's candy canes to jelly beans became 1 : 3. How many jelly beans did Hilda buy?

	Hilda		Simon
	Candy canes	Jelly beans	Candy canes	Jelly beans
Before	1 u + 4	6 u	1 p	3 p + 33
Change	- 4			- 33
After	1 u	6 u	1 p	3 p

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

6 u = 3 p + 33 
6 u - 33 = 3 p --- (1)

1 u + 4 = 1 p --- (2)

Make p the same.

(2)_x3
3 u + 12 = 3 p --- (3)

(1) = (3)
6 u - 33 = 3 u + 12 
6 u - 3 u = 12 + 33
3 u = 45

1 u = 45 ÷ 3 = 15

Number of jelly beans that Hilda bought
= 2 x 6 u
= 12 u
= 12 x 15
= 180

Answer(s): 180