Tim, Sam and Henry had some beads in the ratio of 4 : 5 : 9. Henry gave 50% of his beads to Tim and Sam. As a result, Tim had the same number of beads as Sam and Henry had 45 fewer beads than Tim.
- What was the percentage increase in Tim's beads after receiving from Henry?
- How many beads did Sam have at first?
| Tim |
Sam |
Henry |
Total |
| 4 u |
5 u |
9 u |
18 u |
| + 4.5 u |
- 4.5 u |
|
| 6.75 u |
6.75 u |
4.5 u |
18 u |
(a)
Number of beads that Henry gave away
= 50% x 9
=
50100 x 9
= 4.5 u
Number of beads that Tim and Sam each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u
Increase in the number of beads that Tim had
= 6.75 u - 4 u
= 2.75 u
Percentage increase in Tim's beads after receiving from Henry
=
2.754 x 100%
= 68.75%
(b)
6.75 u = 4.5 u + 45
6.75 u - 4.5 u = 45
2.25 u = 45
1 u = 45 ÷ 2.25 = 20
Number of beads that Sam had at first
= 5 u
= 5 x 20
= 100
Answer(s): (a) 68.75%; (b) 100
