Reggie, Brandon and Billy had some beads in the ratio of 5 : 6 : 11. Billy gave 40% of his beads to Reggie and Brandon. As a result, Reggie had the same number of beads as Brandon and Billy had 22 fewer beads than Reggie.

1. What was the percentage increase in Reggie's beads after receiving from Billy?
2. How many beads did Brandon have at first?

Reggie	Brandon	Billy	Total
5 u	6 u	11 u	22 u
+ 4.4 u		- 4.4 u
7.7 u	7.7 u	6.6 u	22 u

(a)
Number of beads that Billy gave away
= 40% x 11
= ⁴⁰₁₀₀ x 11
= 4.4 u

Number of beads that Reggie and Brandon each had in the end
= (22 u - 6.6 u) ÷ 2
= 15.4 u ÷ 2
= 7.7 u

Increase in the number of beads that Reggie had
= 7.7 u - 5 u
= 2.7 u

Percentage increase in Reggie's beads after receiving from Billy
= ^2.7₅ x 100%
= 54%

(b)
7.7 u = 6.6 u + 22
7.7 u - 6.6 u = 22
1.1 u = 22

1 u = 22 ÷ 1.1 = 20

Number of beads that Brandon had at first
= 6 u
= 6 x 20
= 120

Answer(s): (a) 54%; (b) 120