Jeremy, Bryan and Jack had some buttons in the ratio of 2 : 3 : 5. Jack gave 40% of his buttons to Jeremy and Bryan. As a result, Jeremy had the same number of buttons as Bryan and Jack had 49 fewer buttons than Jeremy.

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

Jeremy	Bryan	Jack	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 Jack gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 49
3.5 u - 3 u = 49
0.5 u = 49

1 u = 49 ÷ 0.5 = 98

Number of buttons that Bryan had at first
= 3 u
= 3 x 98
= 294

Answer(s): (a) 75%; (b) 294