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

1. What was the percentage increase in Charlie's stamps after receiving from Howard?
2. How many stamps did Jack have at first?

Charlie	Jack	Howard	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 Howard gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of stamps that Charlie and Jack 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 Charlie had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Charlie's stamps after receiving from Howard
= ^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 Jack had at first
= 5 u
= 5 x 16
= 80

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