PSLE
Dana bought some sweets and gave half of it to Daniel. Daniel bought some jelly beans and gave half of it to Dana. Dana ate 8 jelly beans and Daniel ate 9 sweets. The ratio of Dana's jelly beans to sweets became 1 : 6 and the ratio of Daniel's jelly beans to sweets became 1 : 3. How many sweets did Dana buy?

	Dana		Daniel
	Jelly beans	Sweets	Jelly beans	Sweets
Before	1 u + 8	6 u	1 p	3 p + 9
Change	- 8			- 9
After	1 u	6 u	1 p	3 p

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

6 u = 3 p + 9 
6 u - 9 = 3 p --- (1)

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

Make p the same.

(2)_x3
3 u + 24 = 3 p --- (3)

(1) = (3)
6 u - 9 = 3 u + 24 
6 u - 3 u = 24 + 9
3 u = 33

1 u = 33 ÷ 3 = 11

Number of sweets that Dana bought
= 2 x 6 u
= 12 u
= 12 x 11
= 132

Answer(s): 132