PSLE
Zoe bought some chocolate bars and gave half of it to Fred. Fred bought some sweets and gave half of it to Zoe. Zoe ate 12 sweets and Fred ate 4 chocolate bars. The ratio of Zoe's sweets to chocolate bars became 1 : 6 and the ratio of Fred's sweets to chocolate bars became 1 : 2. How many sweets did Fred buy?

	Zoe		Fred
	Sweets	Chocolate bars	Sweets	Chocolate bars
Before	1 u + 12	6 u	1 p	2 p + 4
Change	- 12			- 4
After	1 u	6 u	1 p	2 p

After Zoe gave half of the chocolate bars to Fred and Fred gave half of his sweets to Zoe, Fred and Zoe had same number of sweets and chocolate bars before each ate some.

6 u = 2 p + 4 
6 u - 4 = 2 p --- (1)

1 u + 12 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 24 = 2 p --- (3)

(1) = (3)
6 u - 4 = 2 u + 24 
6 u - 2 u = 24 + 4
4 u = 28

1 u = 28 ÷ 4 = 7

1 p
= 1 u + 12
= 7 + 12
= 19

Number of sweets that Fred bought
= 2 p
= 2 x 19
= 38

Answer(s): 38