Penelope had some green and gold beads. If she gives away 45 green beads, the number of green beads will be 20% of the total number of beads left. If she gives away 10 gold beads, the number of green beads will be 25% of the total number of beads left.
- How many beads does Penelope have altogether?
- What fraction of Penelope's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Gold |
Green |
Gold |
| Before |
1 u + 45 |
4 u |
1 p |
3 p + 10 |
| Change |
- 45 |
No change |
No change |
- 10 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 45 = 1 p --- (1)
4 u = 3 p + 10
4 u - 10 = 3 p --- (2)
Make p the same.
(1)
x33 u + 135 = 3 p --- (3)
(2) = (3)
4 u - 10 = 3 u + 135
4 u - 3 u = 135 + 10
1 u = 145
Number of beads that Penelope had at first
= 1 u + 45 + 4 u
= 5 u + 45
= 5 x 145 + 45
= 725 + 45
= 770
(b)
Number of gold beads
= 4 u
= 4 x 145
= 580
Fraction of Penelope's beads that is gold
=
580770=
5877 Answer(s): (a) 770; (b)
5877 
