In January, Risa and Asher had pens in the ratio 15 : 7. In February, each of them gave away the same number of pens. Risa then had four times as many pens as Asher.

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

	Risa	Asher	Difference
Before	15x3 = 45 u	7x3 = 21 u	8x3 = 24 u
Change	- 13 u	- 13 u
After	4x8 = 32 u	1x8 = 8 u	3x8 = 24 u

(a)
Since Risa and Asher gave away the same number of pens, the difference in the number of pens between Risa and Asher at first and in the end remains the same.

Make the difference in the number of pens at first and in the end the same. LCM of 8 and 3 is 24.

Asher's pens in January : Asher's pens in February
21 : 8

(b)
Total number of pens in January
= 45 u + 21 u
= 66 u

Total number of pens in February
= 32 u + 8 u
= 40 u

Total pens in January : Total pens in February
66 : 40 _(÷2)
33 : 20 

Answer(s): (a) 21 : 8; (b) 33 : 20