Michael, Ryan and Owen had some coins in the ratio of 6 : 7 : 13. Owen gave 40% of his coins to Michael and Ryan. As a result, Michael had the same number of coins as Ryan and Owen had 39 fewer coins than Michael.

1. What was the percentage increase in Michael's coins after receiving from Owen?
2. How many coins did Ryan have at first?

Michael	Ryan	Owen	Total
6 u	7 u	13 u	26 u
+ 5.2 u		- 5.2 u
9.1 u	9.1 u	7.8 u	26 u

(a)
Number of coins that Owen gave away
= 40% x 13
= ⁴⁰₁₀₀ x 13
= 5.2 u

Number of coins that Michael and Ryan each had in the end
= (26 u - 7.8 u) ÷ 2
= 18.2 u ÷ 2
= 9.1 u

Increase in the number of coins that Michael had
= 9.1 u - 6 u
= 3.1 u

Percentage increase in Michael's coins after receiving from Owen
= ^3.1₆ x 100%
= 51.666666666667%

(b)
9.1 u = 7.8 u + 39
9.1 u - 7.8 u = 39
1.3 u = 39

1 u = 39 ÷ 1.3 = 30

Number of coins that Ryan had at first
= 7 u
= 7 x 30
= 210

Answer(s): (a) 51.666666666667%; (b) 210