In January, Penelope and Mark had stickers in the ratio 12 : 7. In February, each of them gave away the same number of stickers. Penelope then had thrice as many stickers as Mark.

1. Find the ratio of the number of stickers Mark had in January to the number of stickers he had in February.
2. Find the ratio of the total number of stickers both had in January to the total number of stickers both had in February.

	Penelope	Mark	Difference
Before	12x2 = 24 u	7x2 = 14 u	5x2 = 10 u
Change	- 9 u	- 9 u
After	3x5 = 15 u	1x5 = 5 u	2x5 = 10 u

(a)
Since Penelope and Mark gave away the same number of stickers, the difference in the number of stickers between Penelope and Mark at first and in the end remains the same.

Make the difference in the number of stickers at first and in the end the same. LCM of 5 and 2 is 10.

Mark's stickers in January : Mark's stickers in February
14 : 5

(b)
Total number of stickers in January
= 24 u + 14 u
= 38 u

Total number of stickers in February
= 15 u + 5 u
= 20 u

Total stickers in January : Total stickers in February
38 : 20 _(÷2)
19 : 10 

Answer(s): (a) 14 : 5; (b) 19 : 10