In January, Penelope and Valen had stickers in the ratio 13 : 7. In February, each of them gave away the same number of stickers. Penelope then had five times as many stickers as Valen.

1. Find the ratio of the number of stickers Valen 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	Valen	Difference
Before	13x2 = 26 u	7x2 = 14 u	6x2 = 12 u
Change	- 11 u	- 11 u
After	5x3 = 15 u	1x3 = 3 u	4x3 = 12 u

(a)
Since Penelope and Valen gave away the same number of stickers, the difference in the number of stickers between Penelope and Valen 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 6 and 4 is 12.

Valen's stickers in January : Valen's stickers in February
14 : 3

(b)
Total number of stickers in January
= 26 u + 14 u
= 40 u

Total number of stickers in February
= 15 u + 3 u
= 18 u

Total stickers in January : Total stickers in February
40 : 18 _(÷2)
20 : 9 

Answer(s): (a) 14 : 3; (b) 20 : 9