Zeph, Neave and Luke had some marbles in the ratio of 2 : 3 : 5. Luke gave 50% of his marbles to Zeph and Neave. As a result, Zeph had the same number of marbles as Neave and Luke had 10 fewer marbles than Zeph.

1. What was the percentage increase in Zeph's marbles after receiving from Luke?
2. How many marbles did Neave have at first?

Zeph	Neave	Luke	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 Luke gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of marbles that Zeph and Neave 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 Zeph had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Zeph's marbles after receiving from Luke
= ^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 marbles that Neave had at first
= 3 u
= 3 x 8
= 24

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