Sam, Reggie and Ethan had some marbles in the ratio of 2 : 3 : 5. Ethan gave 40% of his marbles to Sam and Reggie. As a result, Sam had the same number of marbles as Reggie and Ethan had 11 fewer marbles than Sam.

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

Sam	Reggie	Ethan	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 Ethan gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 11
3.5 u - 3 u = 11
0.5 u = 11

1 u = 11 ÷ 0.5 = 22

Number of marbles that Reggie had at first
= 3 u
= 3 x 22
= 66

Answer(s): (a) 75%; (b) 66