Jeremy, Neave and Zeph had some marbles in the ratio of 2 : 3 : 5. Zeph gave 40% of his marbles to Jeremy and Neave. As a result, Jeremy had the same number of marbles as Neave and Zeph had 32 fewer marbles than Jeremy.

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

Jeremy	Neave	Zeph	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 Zeph gave away
= 40% x 5
= ⁴⁰₁₀₀ x 5
= 2 u

Number of marbles that Jeremy and Neave 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 Zeph
= ^1.5₂ x 100%
= 75%

(b)
3.5 u = 3 u + 32
3.5 u - 3 u = 32
0.5 u = 32

1 u = 32 ÷ 0.5 = 64

Number of marbles that Neave had at first
= 3 u
= 3 x 64
= 192

Answer(s): (a) 75%; (b) 192