Albert, Pierre and Tim had some beads in the ratio of 5 : 6 : 11. Tim gave 50% of his beads to Albert and Pierre. As a result, Albert had the same number of beads as Pierre and Tim had 11 fewer beads than Albert.

1. What was the percentage increase in Albert's beads after receiving from Tim?
2. How many beads did Pierre have at first?

Albert	Pierre	Tim	Total
5 u	6 u	11 u	22 u
+ 5.5 u		- 5.5 u
8.25 u	8.25 u	5.5 u	22 u

(a)
Number of beads that Tim gave away
= 50% x 11
= ⁵⁰₁₀₀ x 11
= 5.5 u

Number of beads that Albert and Pierre each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u

Increase in the number of beads that Albert had
= 8.25 u - 5 u
= 3.25 u

Percentage increase in Albert's beads after receiving from Tim
= ^3.25₅ x 100%
= 65%

(b)
8.25 u = 5.5 u + 11
8.25 u - 5.5 u = 11
2.75 u = 11

1 u = 11 ÷ 2.75 = 4

Number of beads that Pierre had at first
= 6 u
= 6 x 4
= 24

Answer(s): (a) 65%; (b) 24