Lynn had some red and black beads. If she gives away 26 red beads, the number of red beads will be 20% of the total number of beads left. If she gives away 24 black beads, the number of red beads will be 25% of the total number of beads left.
- How many beads does Lynn have altogether?
- What fraction of Lynn's beads is black?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Black |
Red |
Black |
| Before |
1 u + 26 |
4 u |
1 p |
3 p + 24 |
| Change |
- 26 |
No change |
No change |
- 24 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 26 = 1 p --- (1)
4 u = 3 p + 24
4 u - 24 = 3 p --- (2)
Make p the same.
(1)
x33 u + 78 = 3 p --- (3)
(2) = (3)
4 u - 24 = 3 u + 78
4 u - 3 u = 78 + 24
1 u = 102
Number of beads that Lynn had at first
= 1 u + 26 + 4 u
= 5 u + 26
= 5 x 102 + 26
= 510 + 26
= 536
(b)
Number of black beads
= 4 u
= 4 x 102
= 408
Fraction of Lynn's beads that is black
=
408536=
5167 Answer(s): (a) 536; (b)
5167 
