PSLE
Kylie bought some chocolate bars and gave half of it to Archie. Archie bought some sweets and gave half of it to Kylie. Kylie ate 2 sweets and Archie ate 2 chocolate bars. The ratio of Kylie's sweets to chocolate bars became 1 : 5 and the ratio of Archie's sweets to chocolate bars became 1 : 3. How many chocolate bars did Kylie buy?

	Kylie		Archie
	Sweets	Chocolate bars	Sweets	Chocolate bars
Before	1 u + 2	5 u	1 p	3 p + 2
Change	- 2			- 2
After	1 u	5 u	1 p	3 p

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

5 u = 3 p + 2 
5 u - 2 = 3 p --- (1)

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

Make p the same.

(2)_x3
3 u + 6 = 3 p --- (3)

(1) = (3)
5 u - 2 = 3 u + 6 
5 u - 3 u = 6 + 2
2 u = 8

1 u = 8 ÷ 2 = 4

Number of chocolate bars that Kylie bought
= 2 x 5 u
= 10 u
= 10 x 4
= 40

Answer(s): 40