Pierre, Ethan and Charlie had some marbles in the ratio of 2 : 3 : 5. Charlie gave 40% of his marbles to Pierre and Ethan. As a result, Pierre had the same number of marbles as Ethan and Charlie had 48 fewer marbles than Pierre.

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

Pierre	Ethan	Charlie	Total
2 u	3 u	5 u	10 u
+ 2 u		- 2 u
3.5 u	3.5 u	3 u	10 u

(a)
Number of marbles that Charlie gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of marbles that Pierre and Ethan each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u

Increase in the number of marbles that Pierre had
= 3.5 u - 2 u
= 1.5 u

Percentage increase in Pierre's marbles after receiving from Charlie
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 48
3.5 u - 3 u = 48
0.5 u = 48

1 u = 48 ÷ 0.5 = 96

Number of marbles that Ethan had at first
= 3 u
= 3 x 96
= 288

Answer(s): (a) 75%; (b) 288