Eric, Julian and Fabian had some buttons in the ratio of 3 : 4 : 7. Fabian gave 40% of his buttons to Eric and Julian. As a result, Eric had the same number of buttons as Julian and Fabian had 28 fewer buttons than Eric.

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

Eric	Julian	Fabian	Total
3 u	4 u	7 u	14 u
+ 2.8 u		- 2.8 u
4.9 u	4.9 u	4.2 u	14 u

(a)
Number of buttons that Fabian gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of buttons that Eric and Julian each had in the end
= (14 u - 4.2 u) ÷ 2
= 9.8 u ÷ 2
= 4.9 u

Increase in the number of buttons that Eric had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Eric's buttons after receiving from Fabian
= ^1.9₃ x 100%
= 63.333333333333%

(b)
4.9 u = 4.2 u + 28
4.9 u - 4.2 u = 28
0.7 u = 28

1 u = 28 ÷ 0.7 = 40

Number of buttons that Julian had at first
= 4 u
= 4 x 40
= 160

Answer(s): (a) 63.333333333333%; (b) 160