Caden, Ian and Ethan had some marbles in the ratio of 2 : 3 : 5. Ethan gave 50% of his marbles to Caden and Ian. As a result, Caden had the same number of marbles as Ian and Ethan had 15 fewer marbles than Caden.

1. What was the percentage increase in Caden's marbles after receiving from Ethan?
2. How many marbles did Ian have at first?

Caden	Ian	Ethan	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 marbles that Ethan gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of marbles that Caden and Ian each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of marbles that Caden had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Caden's marbles after receiving from Ethan
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 15
3.75 u - 2.5 u = 15
1.25 u = 15

1 u = 15 ÷ 1.25 = 12

Number of marbles that Ian had at first
= 3 u
= 3 x 12
= 36

Answer(s): (a) 87.5%; (b) 36