In January, Fiona and Tom had pens in the ratio 9 : 4. In February, each of them gave away the same number of pens. Fiona then had thrice as many pens as Tom.

1. Find the ratio of the number of pens Tom 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.

	Fiona	Tom	Difference
Before	9x2 = 18 u	4x2 = 8 u	5x2 = 10 u
Change	- 3 u	- 3 u
After	3x5 = 15 u	1x5 = 5 u	2x5 = 10 u

(a)
Since Fiona and Tom gave away the same number of pens, the difference in the number of pens between Fiona and Tom 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 2 is 10.

Tom's pens in January : Tom's pens in February
8 : 5

(b)
Total number of pens in January
= 18 u + 8 u
= 26 u

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

Total pens in January : Total pens in February
26 : 20 _(÷2)
13 : 10 

Answer(s): (a) 8 : 5; (b) 13 : 10