Owen, Pierre and Nick had some beads in the ratio of 2 : 3 : 5. Nick gave 40% of his beads to Owen and Pierre. As a result, Owen had the same number of beads as Pierre and Nick had 42 fewer beads than Owen.
- What was the percentage increase in Owen's beads after receiving from Nick?
- How many beads did Pierre have at first?
| Owen |
Pierre |
Nick |
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 Nick gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of beads that Owen and Pierre each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of beads that Owen had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Owen's beads after receiving from Nick
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 42
3.5 u - 3 u = 42
0.5 u = 42
1 u = 42 ÷ 0.5 = 84
Number of beads that Pierre had at first
= 3 u
= 3 x 84
= 252
Answer(s): (a) 75%; (b) 252
