Eva had some white and gold beads. If she gives away 22 white beads, the number of white beads will be 20% of the total number of beads left. If she gives away 44 gold beads, the number of white beads will be 25% of the total number of beads left.
- How many beads does Eva have altogether?
- What fraction of Eva's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
White |
Gold |
White |
Gold |
| Before |
1 u + 22 |
4 u |
1 p |
3 p + 44 |
| Change |
- 22 |
No change |
No change |
- 44 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 22 = 1 p --- (1)
4 u = 3 p + 44
4 u - 44 = 3 p --- (2)
Make p the same.
(1)
x33 u + 66 = 3 p --- (3)
(2) = (3)
4 u - 44 = 3 u + 66
4 u - 3 u = 66 + 44
1 u = 110
Number of beads that Eva had at first
= 1 u + 22 + 4 u
= 5 u + 22
= 5 x 110 + 22
= 550 + 22
= 572
(b)
Number of gold beads
= 4 u
= 4 x 110
= 440
Fraction of Eva's beads that is gold
=
440572=
1013 Answer(s): (a) 572; (b)
1013 
