Elijah, Nick and Bryan had some buttons in the ratio of 2 : 3 : 5. Bryan gave 50% of his buttons to Elijah and Nick. As a result, Elijah had the same number of buttons as Nick and Bryan had 30 fewer buttons than Elijah.

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

Elijah	Nick	Bryan	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of buttons that Bryan gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of buttons that Elijah and Nick each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of buttons that Elijah had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Elijah's buttons after receiving from Bryan
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 30
3.75 u - 2.5 u = 30
1.25 u = 30

1 u = 30 ÷ 1.25 = 24

Number of buttons that Nick had at first
= 3 u
= 3 x 24
= 72

Answer(s): (a) 87.5%; (b) 72