PSLE
Gabby bought some chocolate bars and gave half of it to Archie. Archie bought some candy canes and gave half of it to Gabby. Gabby ate 6 candy canes and Archie ate 4 chocolate bars. The ratio of Gabby's candy canes to chocolate bars became 1 : 6 and the ratio of Archie's candy canes to chocolate bars became 1 : 2. How many candy canes did Archie buy?

	Gabby		Archie
	Candy canes	Chocolate bars	Candy canes	Chocolate bars
Before	1 u + 6	6 u	1 p	2 p + 4
Change	- 6			- 4
After	1 u	6 u	1 p	2 p

After Gabby gave half of the chocolate bars to Archie and Archie gave half of his candy canes to Gabby, Archie and Gabby had same number of candy canes and chocolate bars before each ate some.

6 u = 2 p + 4 
6 u - 4 = 2 p --- (1)

1 u + 6 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 12 = 2 p --- (3)

(1) = (3)
6 u - 4 = 2 u + 12 
6 u - 2 u = 12 + 4
4 u = 16

1 u = 16 ÷ 4 = 4

1 p
= 1 u + 6
= 4 + 6
= 10

Number of candy canes that Archie bought
= 2 p
= 2 x 10
= 20

Answer(s): 20