George, Elijah and Andy had some beads in the ratio of 2 : 3 : 5. Andy gave 50% of his beads to George and Elijah. As a result, George had the same number of beads as Elijah and Andy had 30 fewer beads than George.

1. What was the percentage increase in George's beads after receiving from Andy?
2. How many beads did Elijah have at first?

George	Elijah	Andy	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 Andy gave away
= 50% x 5
= ⁵⁰₁₀₀ x 5
= 2.5 u

Number of beads that George and Elijah 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 George had
= 3.75 u - 2 u
= 1.75 u

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

(b)
3.75 u = 2.5 u + 30
3.75 u - 2.5 u = 30
1.25 u = 30

1 u = 30 ÷ 1.25 = 24

Number of beads that Elijah had at first
= 3 u
= 3 x 24
= 72

Answer(s): (a) 87.5%; (b) 72