Brandon, Nick and Reggie had some coins in the ratio of 5 : 6 : 11. Reggie gave 50% of his coins to Brandon and Nick. As a result, Brandon had the same number of coins as Nick and Reggie had 11 fewer coins than Brandon.

1. What was the percentage increase in Brandon's coins after receiving from Reggie?
2. How many coins did Nick have at first?

Brandon	Nick	Reggie	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of coins that Reggie gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of coins that Brandon and Nick each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of coins that Brandon had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Brandon's coins after receiving from Reggie
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of coins that Nick had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24