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

1. What was the percentage increase in Oscar's beads after receiving from Ryan?
2. How many beads did Perry have at first?

Oscar	Perry	Ryan	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 beads that Ryan gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of beads that Oscar and Perry each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of beads that Oscar had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Oscar's beads after receiving from Ryan
= ^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 beads that Perry had at first
= 5 u
= 5 x 8
= 40

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