Zoe had some purple and silver beads. If she gives away 39 purple beads, the number of purple beads will be 10% of the total number of beads left. If she gives away 39 silver beads, the number of purple beads will be 25% of the total number of beads left.
- How many beads does Zoe have altogether?
- What fraction of Zoe's beads is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Purple |
Silver |
Purple |
Silver |
| Before |
1 u + 39 |
9 u |
1 p |
3 p + 39 |
| Change |
- 39 |
No change |
No change |
- 39 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 39 = 1 p --- (1)
9 u = 3 p + 39
9 u - 39 = 3 p --- (2)
Make p the same.
(1)
x33 u + 117 = 3 p --- (3)
(2) = (3)
9 u - 39 = 3 u + 117
9 u - 3 u = 117 + 39
6 u = 156
1 u = 156 ÷ 6 = 26
Number of beads that Zoe had at first
= 1 u + 39 + 9 u
= 10 u + 39
= 10 x 26 + 39
= 260 + 39
= 299
(b)
Number of silver beads
= 9 u
= 9 x 26
= 234
Fraction of Zoe's beads that is silver
=
234299=
1823 Answer(s): (a) 299; (b)
1823 
