Luke, Oscar and Japheth had some coins in the ratio of 4 : 5 : 9. Japheth gave 50% of his coins to Luke and Oscar. As a result, Luke had the same number of coins as Oscar and Japheth had 18 fewer coins than Luke.

1. What was the percentage increase in Luke's coins after receiving from Japheth?
2. How many coins did Oscar have at first?

Luke	Oscar	Japheth	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 Japheth gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of coins that Luke and Oscar 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 Luke had
= 6.75 u - 4 u
= 2.75 u

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

(b)
6.75 u = 4.5 u + 18
6.75 u - 4.5 u = 18
2.25 u = 18

1 u = 18 ÷ 2.25 = 8

Number of coins that Oscar had at first
= 5 u
= 5 x 8
= 40

Answer(s): (a) 68.75%; (b) 40