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

1. What was the percentage increase in Gabriel's buttons after receiving from Jeremy?
2. How many buttons did Sean have at first?

Gabriel	Sean	Jeremy	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 Jeremy gave away
= 40% x 7
= ⁴⁰₁₀₀ x 7
= 2.8 u

Number of buttons that Gabriel and Sean 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 Gabriel had
= 4.9 u - 3 u
= 1.9 u

Percentage increase in Gabriel's buttons after receiving from Jeremy
= ^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 Sean had at first
= 4 u
= 4 x 40
= 160

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