Tommy, Fabian and Mark had some pens in the ratio of 3 : 4 : 7. Mark gave 50% of his pens to Tommy and Fabian. As a result, Tommy had the same number of pens as Fabian and Mark had 14 fewer pens than Tommy.

1. What was the percentage increase in Tommy's pens after receiving from Mark?
2. How many pens did Fabian have at first?

Tommy	Fabian	Mark	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of pens that Mark gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of pens that Tommy and Fabian each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of pens that Tommy had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Tommy's pens after receiving from Mark
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 14
5.25 u - 3.5 u = 14
1.75 u = 14

1 u = 14 ÷ 1.75 = 8

Number of pens that Fabian had at first
= 4 u
= 4 x 8
= 32

Answer(s): (a) 75%; (b) 32