Fabian, Andy and Vincent had some buttons in the ratio of 2 : 3 : 5. Vincent gave 40% of his buttons to Fabian and Andy. As a result, Fabian had the same number of buttons as Andy and Vincent had 36 fewer buttons than Fabian.

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

Fabian	Andy	Vincent	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 Vincent gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 36
3.5 u - 3 u = 36
0.5 u = 36

1 u = 36 ÷ 0.5 = 72

Number of buttons that Andy had at first
= 3 u
= 3 x 72
= 216

Answer(s): (a) 75%; (b) 216