Sam, Bobby and George had some beads in the ratio of 5 : 6 : 11. George gave 40% of his beads to Sam and Bobby. As a result, Sam had the same number of beads as Bobby and George had 11 fewer beads than Sam.

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

Sam	Bobby	George	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 George gave away
= 40% x 11
= ⁴⁰₁₀₀ x 11
= 4.4 u

Number of beads that Sam and Bobby 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 Sam had
= 7.7 u - 5 u
= 2.7 u

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

(b)
7.7 u = 6.6 u + 11
7.7 u - 6.6 u = 11
1.1 u = 11

1 u = 11 ÷ 1.1 = 10

Number of beads that Bobby had at first
= 6 u
= 6 x 10
= 60

Answer(s): (a) 54%; (b) 60