Bobby, Gabriel and Michael had some beads in the ratio of 4 : 5 : 9. Michael gave 40% of his beads to Bobby and Gabriel. As a result, Bobby had the same number of beads as Gabriel and Michael had 27 fewer beads than Bobby.

1. What was the percentage increase in Bobby's beads after receiving from Michael?
2. How many beads did Gabriel have at first?

Bobby	Gabriel	Michael	Total
4 u	5 u	9 u	18 u
+ 3.6 u		- 3.6 u
6.3 u	6.3 u	5.4 u	18 u

(a)
Number of beads that Michael gave away
= 40% x 9
= ⁴⁰₁₀₀ x 9
= 3.6 u

Number of beads that Bobby and Gabriel each had in the end
= (18 u - 5.4 u) ÷ 2
= 12.6 u ÷ 2
= 6.3 u

Increase in the number of beads that Bobby had
= 6.3 u - 4 u
= 2.3 u

Percentage increase in Bobby's beads after receiving from Michael
= ^2.3₄ x 100%
= 57.5%

(b)
6.3 u = 5.4 u + 27
6.3 u - 5.4 u = 27
0.9 u = 27

1 u = 27 ÷ 0.9 = 30

Number of beads that Gabriel had at first
= 5 u
= 5 x 30
= 150

Answer(s): (a) 57.5%; (b) 150