Jeremy, Will and Dylan had some marbles in the ratio of 2 : 3 : 5. Dylan gave 40% of his marbles to Jeremy and Will. As a result, Jeremy had the same number of marbles as Will and Dylan had 15 fewer marbles than Jeremy.

1. What was the percentage increase in Jeremy's marbles after receiving from Dylan?
2. How many marbles did Will have at first?

Jeremy	Will	Dylan	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 Dylan gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

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

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

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

(b)
3.5 u = 3 u + 15
3.5 u - 3 u = 15
0.5 u = 15

1 u = 15 ÷ 0.5 = 30

Number of marbles that Will had at first
= 3 u
= 3 x 30
= 90

Answer(s): (a) 75%; (b) 90