Paul, Billy and George had some erasers in the ratio of 4 : 5 : 9. George gave 50% of his erasers to Paul and Billy. As a result, Paul had the same number of erasers as Billy and George had 45 fewer erasers than Paul.

1. What was the percentage increase in Paul's erasers after receiving from George?
2. How many erasers did Billy have at first?

Paul	Billy	George	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 erasers that George gave away
= 50% x 9
= ⁵⁰₁₀₀ x 9
= 4.5 u

Number of erasers that Paul and Billy each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u

Increase in the number of erasers that Paul had
= 6.75 u - 4 u
= 2.75 u

Percentage increase in Paul's erasers after receiving from George
= ^2.75₄ x 100%
= 68.75%

(b)
6.75 u = 4.5 u + 45
6.75 u - 4.5 u = 45
2.25 u = 45

1 u = 45 ÷ 2.25 = 20

Number of erasers that Billy had at first
= 5 u
= 5 x 20
= 100

Answer(s): (a) 68.75%; (b) 100