Elijah, Luis and Bobby had some erasers in the ratio of 2 : 3 : 5. Bobby gave 50% of his erasers to Elijah and Luis. As a result, Elijah had the same number of erasers as Luis and Bobby had 40 fewer erasers than Elijah.

1. What was the percentage increase in Elijah's erasers after receiving from Bobby?
2. How many erasers did Luis have at first?

Elijah	Luis	Bobby	Total
2 u	3 u	5 u	10 u
+ 2.5 u		- 2.5 u
3.75 u	3.75 u	2.5 u	10 u

(a)
Number of erasers that Bobby gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of erasers that Elijah and Luis each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of erasers that Elijah had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Elijah's erasers after receiving from Bobby
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of erasers that Luis had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96