Julian, Perry and Billy had some erasers in the ratio of 5 : 6 : 11. Billy gave 50% of his erasers to Julian and Perry. As a result, Julian had the same number of erasers as Perry and Billy had 11 fewer erasers than Julian.

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

Julian	Perry	Billy	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of erasers that Billy gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of erasers that Julian and Perry each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of erasers that Julian had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Julian's erasers after receiving from Billy
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of erasers that Perry had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24