Valen, Will and John had some coins in the ratio of 4 : 5 : 9. John gave 50% of his coins to Valen and Will. As a result, Valen had the same number of coins as Will and John had 27 fewer coins than Valen.

1. What was the percentage increase in Valen's coins after receiving from John?
2. How many coins did Will have at first?

Valen	Will	John	Total
4 u	5 u	9 u	18 u
+ 4.5 u		- 4.5 u
6.75 u	6.75 u	4.5 u	18 u

(a)
Number of coins that John gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of coins that Valen and Will each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of coins that Valen had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Valen's coins after receiving from John
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 27
6.75 u - 4.5 u = 27
2.25 u = 27

1 u = 27 ÷ 2.25 = 12

Number of coins that Will had at first
= 5 u
= 5 x 12
= 60

Answer(s): (a) 68.75%; (b) 60