Owen, Reggie and Ben had some buttons in the ratio of 2 : 3 : 5. Ben gave 50% of his buttons to Owen and Reggie. As a result, Owen had the same number of buttons as Reggie and Ben had 40 fewer buttons than Owen.

1. What was the percentage increase in Owen's buttons after receiving from Ben?
2. How many buttons did Reggie have at first?

Owen	Reggie	Ben	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of buttons that Ben gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of buttons that Owen and Reggie each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of buttons that Owen had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Owen's buttons after receiving from Ben
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of buttons that Reggie had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96