Fabian, Andy and Owen had some beads in the ratio of 2 : 3 : 5. Owen gave 40% of his beads to Fabian and Andy. As a result, Fabian had the same number of beads as Andy and Owen had 48 fewer beads than Fabian.
- What was the percentage increase in Fabian's beads after receiving from Owen?
- How many beads did Andy have at first?
| Fabian |
Andy |
Owen |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of beads that Owen gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Fabian and Andy each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Fabian had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Fabian's beads after receiving from Owen
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 48
3.5 u - 3 u = 48
0.5 u = 48
1 u = 48 ÷ 0.5 = 96
Number of beads that Andy had at first
= 3 u
= 3 x 96
= 288
Answer(s): (a) 75%; (b) 288
