Jack, Fabian and Lee had some buttons in the ratio of 2 : 3 : 5. Lee gave 40% of his buttons to Jack and Fabian. As a result, Jack had the same number of buttons as Fabian and Lee had 43 fewer buttons than Jack.

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

Jack	Fabian	Lee	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 Lee gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 43
3.5 u - 3 u = 43
0.5 u = 43

1 u = 43 ÷ 0.5 = 86

Number of buttons that Fabian had at first
= 3 u
= 3 x 86
= 258

Answer(s): (a) 75%; (b) 258