Penelope had some green and purple beads. If she gives away 15 green beads, the number of green beads will be 20% of the total number of beads left. If she gives away 50 purple 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 purple?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Purple |
Green |
Purple |
| Before |
1 u + 15 |
4 u |
1 p |
3 p + 50 |
| Change |
- 15 |
No change |
No change |
- 50 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 15 = 1 p --- (1)
4 u = 3 p + 50
4 u - 50 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
4 u - 50 = 3 u + 45
4 u - 3 u = 45 + 50
1 u = 95
Number of beads that Penelope had at first
= 1 u + 15 + 4 u
= 5 u + 15
= 5 x 95 + 15
= 475 + 15
= 490
(b)
Number of purple beads
= 4 u
= 4 x 95
= 380
Fraction of Penelope's beads that is purple
=
380490=
3849 Answer(s): (a) 490; (b)
3849 
