Cindy had some black and brown beads. If she gives away 31 black beads, the number of black beads will be 20% of the total number of beads left. If she gives away 31 brown beads, the number of black beads will be 25% of the total number of beads left.
- How many beads does Cindy have altogether?
- What fraction of Cindy's beads is brown?
| |
Scenario 1 |
Scenario 2 |
| |
Black |
Brown |
Black |
Brown |
| Before |
1 u + 31 |
4 u |
1 p |
3 p + 31 |
| Change |
- 31 |
No change |
No change |
- 31 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 31 = 1 p --- (1)
4 u = 3 p + 31
4 u - 31 = 3 p --- (2)
Make p the same.
(1)
x33 u + 93 = 3 p --- (3)
(2) = (3)
4 u - 31 = 3 u + 93
4 u - 3 u = 93 + 31
1 u = 124
Number of beads that Cindy had at first
= 1 u + 31 + 4 u
= 5 u + 31
= 5 x 124 + 31
= 620 + 31
= 651
(b)
Number of brown beads
= 4 u
= 4 x 124
= 496
Fraction of Cindy's beads that is brown
=
496651=
1621 Answer(s): (a) 651; (b)
1621 
