In February, Betty and Fabian had pens in the ratio 14 : 9. In March, each of them gave away the same number of pens. Betty then had five times as many pens as Fabian.

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

	Betty	Fabian	Difference
Before	14x4 = 56 u	9x4 = 36 u	5x4 = 20 u
Change	- 31 u	- 31 u
After	5x5 = 25 u	1x5 = 5 u	4x5 = 20 u

(a)
Since Betty and Fabian gave away the same number of pens, the difference in the number of pens between Betty and Fabian 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 5 and 4 is 20.

Fabian's pens in February : Fabian's pens in March
36 : 5

(b)
Total number of pens in February
= 56 u + 36 u
= 92 u

Total number of pens in March
= 25 u + 5 u
= 30 u

Total pens in February : Total pens in March
92 : 30 _(÷2)
46 : 15 

Answer(s): (a) 36 : 5; (b) 46 : 15