Fabian, Michael and George had some buttons in the ratio of 3 : 4 : 7. George gave 50% of his buttons to Fabian and Michael. As a result, Fabian had the same number of buttons as Michael and George had 35 fewer buttons than Fabian.

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

Fabian	Michael	George	Total
3 u	4 u	7 u	14 u
+ 3.5 u		- 3.5 u
5.25 u	5.25 u	3.5 u	14 u

(a)
Number of buttons that George gave away
= 50% x 7
= ⁵⁰₁₀₀ x 7
= 3.5 u

Number of buttons that Fabian and Michael each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u

Increase in the number of buttons that Fabian had
= 5.25 u - 3 u
= 2.25 u

Percentage increase in Fabian's buttons after receiving from George
= ^2.25₃ x 100%
= 75%

(b)
5.25 u = 3.5 u + 35
5.25 u - 3.5 u = 35
1.75 u = 35

1 u = 35 ÷ 1.75 = 20

Number of buttons that Michael had at first
= 4 u
= 4 x 20
= 80

Answer(s): (a) 75%; (b) 80