Paul, Glen and Bobby had some beads in the ratio of 2 : 3 : 5. Bobby gave 40% of his beads to Paul and Glen. As a result, Paul had the same number of beads as Glen and Bobby had 38 fewer beads than Paul.
- What was the percentage increase in Paul's beads after receiving from Bobby?
- How many beads did Glen have at first?
| Paul |
Glen |
Bobby |
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 Bobby gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Paul and Glen each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Paul had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Paul's beads after receiving from Bobby
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 38
3.5 u - 3 u = 38
0.5 u = 38
1 u = 38 ÷ 0.5 = 76
Number of beads that Glen had at first
= 3 u
= 3 x 76
= 228
Answer(s): (a) 75%; (b) 228
