Wesley, Bryan and Tim had some pens in the ratio of 4 : 5 : 9. Tim gave 50% of his pens to Wesley and Bryan. As a result, Wesley had the same number of pens as Bryan and Tim had 45 fewer pens than Wesley.

1. What was the percentage increase in Wesley's pens after receiving from Tim?
2. How many pens did Bryan have at first?

Wesley	Bryan	Tim	Total
4 u	5 u	9 u	18 u
+ 4.5 u		- 4.5 u
6.75 u	6.75 u	4.5 u	18 u

(a)
Number of pens that Tim gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of pens that Wesley and Bryan each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of pens that Wesley had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Wesley's pens after receiving from Tim
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 45
6.75 u - 4.5 u = 45
2.25 u = 45

1 u = 45 ÷ 2.25 = 20

Number of pens that Bryan had at first
= 5 u
= 5 x 20
= 100

Answer(s): (a) 68.75%; (b) 100