Anna had some white and brown beads. If she gives away 19 white beads, the number of white beads will be 10% of the total number of beads left. If she gives away 45 brown beads, the number of white beads will be 25% of the total number of beads left.
- How many beads does Anna have altogether?
- What fraction of Anna's beads is brown?
| |
Scenario 1 |
Scenario 2 |
| |
White |
Brown |
White |
Brown |
| Before |
1 u + 19 |
9 u |
1 p |
3 p + 45 |
| Change |
- 19 |
No change |
No change |
- 45 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 19 = 1 p --- (1)
9 u = 3 p + 45
9 u - 45 = 3 p --- (2)
Make p the same.
(1)
x33 u + 57 = 3 p --- (3)
(2) = (3)
9 u - 45 = 3 u + 57
9 u - 3 u = 57 + 45
6 u = 102
1 u = 102 ÷ 6 = 17
Number of beads that Anna had at first
= 1 u + 19 + 9 u
= 10 u + 19
= 10 x 17 + 19
= 170 + 19
= 189
(b)
Number of brown beads
= 9 u
= 9 x 17
= 153
Fraction of Anna's beads that is brown
=
153189=
1721 Answer(s): (a) 189; (b)
1721 
