Lee, Liam and Vincent had some beads in the ratio of 5 : 6 : 11. Vincent gave 40% of his beads to Lee and Liam. As a result, Lee had the same number of beads as Liam and Vincent had 33 fewer beads than Lee.

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

Lee	Liam	Vincent	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 Vincent gave away
= 40% x 11
= ⁴⁰₁₀₀ x 11
= 4.4 u

Number of beads that Lee and Liam 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 Lee had
= 7.7 u - 5 u
= 2.7 u

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

(b)
7.7 u = 6.6 u + 33
7.7 u - 6.6 u = 33
1.1 u = 33

1 u = 33 ÷ 1.1 = 30

Number of beads that Liam had at first
= 6 u
= 6 x 30
= 180

Answer(s): (a) 54%; (b) 180