Cole, Rael and Glen had some erasers in the ratio of 2 : 3 : 5. Glen gave 50% of his erasers to Cole and Rael. As a result, Cole had the same number of erasers as Rael and Glen had 10 fewer erasers than Cole.

1. What was the percentage increase in Cole's erasers after receiving from Glen?
2. How many erasers did Rael have at first?

Cole	Rael	Glen	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 Glen gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of erasers that Cole and Rael 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 Cole had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 10
3.75 u - 2.5 u = 10
1.25 u = 10

1 u = 10 ÷ 1.25 = 8

Number of erasers that Rael had at first
= 3 u
= 3 x 8
= 24

Answer(s): (a) 87.5%; (b) 24