Xavier, Mark and Fabian had some stamps in the ratio of 4 : 5 : 9. Fabian gave 50% of his stamps to Xavier and Mark. As a result, Xavier had the same number of stamps as Mark and Fabian had 36 fewer stamps than Xavier.

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

Xavier	Mark	Fabian	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 stamps that Fabian gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of stamps that Xavier and Mark each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of stamps that Xavier had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Xavier's stamps after receiving from Fabian
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 36
6.75 u - 4.5 u = 36
2.25 u = 36

1 u = 36 ÷ 2.25 = 16

Number of stamps that Mark had at first
= 5 u
= 5 x 16
= 80

Answer(s): (a) 68.75%; (b) 80