PSLE
Lynn bought some candy canes and gave half of it to Mark. Mark bought some lollipops and gave half of it to Lynn. Lynn ate 4 lollipops and Mark ate 52 candy canes. The ratio of Lynn's lollipops to candy canes became 1 : 6 and the ratio of Mark's lollipops to candy canes became 1 : 2. How many lollipops did Mark buy?

	Lynn		Mark
	Lollipops	Candy canes	Lollipops	Candy canes
Before	1 u + 4	6 u	1 p	2 p + 52
Change	- 4			- 52
After	1 u	6 u	1 p	2 p

After Lynn gave half of the candy canes to Mark and Mark gave half of his lollipops to Lynn, Mark and Lynn had same number of lollipops and candy canes before each ate some.

6 u = 2 p + 52 
6 u - 52 = 2 p --- (1)

1 u + 4 = 1 p --- (2)

Make p the same.

(2)_x2
2 u + 8 = 2 p --- (3)

(1) = (3)
6 u - 52 = 2 u + 8 
6 u - 2 u = 8 + 52
4 u = 60

1 u = 60 ÷ 4 = 15

1 p
= 1 u + 4
= 15 + 4
= 19

Number of lollipops that Mark bought
= 2 p
= 2 x 19
= 38

Answer(s): 38