Tim, Peter and Lee had some beads in the ratio of 5 : 6 : 11. Lee gave 50% of his beads to Tim and Peter. As a result, Tim had the same number of beads as Peter and Lee had 44 fewer beads than Tim.
- What was the percentage increase in Tim's beads after receiving from Lee?
- How many beads did Peter have at first?
| Tim |
Peter |
Lee |
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 Lee gave away
= 50% x 11
=
50100 x 11
= 5.5 u
Number of beads that Tim and Peter 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 Tim had
= 8.25 u - 5 u
= 3.25 u
Percentage increase in Tim's beads after receiving from Lee
=
3.255 x 100%
= 65%
(b)
8.25 u = 5.5 u + 44
8.25 u - 5.5 u = 44
2.75 u = 44
1 u = 44 ÷ 2.75 = 16
Number of beads that Peter had at first
= 6 u
= 6 x 16
= 96
Answer(s): (a) 65%; (b) 96
