PSLE
Natalie bought some sweets and gave half of it to Oliver. Oliver bought some candy canes and gave half of it to Natalie. Natalie ate 2 candy canes and Oliver ate 41 sweets. The ratio of Natalie's candy canes to sweets became 1 : 5 and the ratio of Oliver's candy canes to sweets became 1 : 2. How many sweets did Natalie buy?

	Natalie		Oliver
	Candy canes	Sweets	Candy canes	Sweets
Before	1 u + 2	5 u	1 p	2 p + 41
Change	- 2			- 41
After	1 u	5 u	1 p	2 p

After Natalie gave half of the sweets to Oliver and Oliver gave half of his candy canes to Natalie, Oliver and Natalie had same number of candy canes and sweets before each ate some.

5 u = 2 p + 41 
5 u - 41 = 2 p --- (1)

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

Make p the same.

(2)_x2
2 u + 4 = 2 p --- (3)

(1) = (3)
5 u - 41 = 2 u + 4 
5 u - 2 u = 4 + 41
3 u = 45

1 u = 45 ÷ 3 = 15

Number of sweets that Natalie bought
= 2 x 5 u
= 10 u
= 10 x 15
= 150

Answer(s): 150