Cathy had some white and blue beads. If she gives away 20 white beads, the number of white beads will be 20% of the total number of beads left. If she gives away 48 blue beads, the number of white beads will be 25% of the total number of beads left.
- How many beads does Cathy have altogether?
- What fraction of Cathy's beads is blue?
| |
Scenario 1 |
Scenario 2 |
| |
White |
Blue |
White |
Blue |
| Before |
1 u + 20 |
4 u |
1 p |
3 p + 48 |
| Change |
- 20 |
No change |
No change |
- 48 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 20 = 1 p --- (1)
4 u = 3 p + 48
4 u - 48 = 3 p --- (2)
Make p the same.
(1)
x33 u + 60 = 3 p --- (3)
(2) = (3)
4 u - 48 = 3 u + 60
4 u - 3 u = 60 + 48
1 u = 108
Number of beads that Cathy had at first
= 1 u + 20 + 4 u
= 5 u + 20
= 5 x 108 + 20
= 540 + 20
= 560
(b)
Number of blue beads
= 4 u
= 4 x 108
= 432
Fraction of Cathy's beads that is blue
=
432560=
2735 Answer(s): (a) 560; (b)
2735 
