Andy, Eric and Owen had some buttons in the ratio of 2 : 3 : 5. Owen gave 40% of his buttons to Andy and Eric. As a result, Andy had the same number of buttons as Eric and Owen had 21 fewer buttons than Andy.

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

Andy	Eric	Owen	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of buttons that Owen gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of buttons that Andy and Eric each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of buttons that Andy had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Andy's buttons after receiving from Owen
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 21
3.5 u - 3 u = 21
0.5 u = 21

1 u = 21 ÷ 0.5 = 42

Number of buttons that Eric had at first
= 3 u
= 3 x 42
= 126

Answer(s): (a) 75%; (b) 126