Oliver, Michael and Oscar had some buttons in the ratio of 4 : 5 : 9. Oscar gave 50% of his buttons to Oliver and Michael. As a result, Oliver had the same number of buttons as Michael and Oscar had 36 fewer buttons than Oliver.

1. What was the percentage increase in Oliver's buttons after receiving from Oscar?
2. How many buttons did Michael have at first?

Oliver	Michael	Oscar	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 buttons that Oscar gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of buttons that Oliver and Michael each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of buttons that Oliver had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Oliver's buttons after receiving from Oscar
= ^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 buttons that Michael had at first
= 5 u
= 5 x 16
= 80

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