Neave, Lee and Zeph had some beads in the ratio of 2 : 3 : 5. Zeph gave 50% of his beads to Neave and Lee. As a result, Neave had the same number of beads as Lee and Zeph had 40 fewer beads than Neave.

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

Neave	Lee	Zeph	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 beads that Zeph gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of beads that Neave and Lee each had in the end
= (10 u - 2.5 u) ÷ 2
= 7.5 u ÷ 2
= 3.75 u

Increase in the number of beads that Neave had
= 3.75 u - 2 u
= 1.75 u

Percentage increase in Neave's beads after receiving from Zeph
= ^1.75₂ x 100%
= 87.5%

(b)
3.75 u = 2.5 u + 40
3.75 u - 2.5 u = 40
1.25 u = 40

1 u = 40 ÷ 1.25 = 32

Number of beads that Lee had at first
= 3 u
= 3 x 32
= 96

Answer(s): (a) 87.5%; (b) 96