Valen, Nick and Luke had some beads in the ratio of 2 : 3 : 5. Luke gave 40% of his beads to Valen and Nick. As a result, Valen had the same number of beads as Nick and Luke had 39 fewer beads than Valen.
- What was the percentage increase in Valen's beads after receiving from Luke?
- How many beads did Nick have at first?
| Valen |
Nick |
Luke |
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 Luke gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Valen and Nick each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Valen had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Valen's beads after receiving from Luke
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 39
3.5 u - 3 u = 39
0.5 u = 39
1 u = 39 ÷ 0.5 = 78
Number of beads that Nick had at first
= 3 u
= 3 x 78
= 234
Answer(s): (a) 75%; (b) 234
