Hilda had some purple and black beads. If she gives away 15 purple beads, the number of purple beads will be 10% of the total number of beads left. If she gives away 27 black beads, the number of purple beads will be 25% of the total number of beads left.
- How many beads does Hilda have altogether?
- What fraction of Hilda's beads is black?
| |
Scenario 1 |
Scenario 2 |
| |
Purple |
Black |
Purple |
Black |
| Before |
1 u + 15 |
9 u |
1 p |
3 p + 27 |
| Change |
- 15 |
No change |
No change |
- 27 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 15 = 1 p --- (1)
9 u = 3 p + 27
9 u - 27 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
9 u - 27 = 3 u + 45
9 u - 3 u = 45 + 27
6 u = 72
1 u = 72 ÷ 6 = 12
Number of beads that Hilda had at first
= 1 u + 15 + 9 u
= 10 u + 15
= 10 x 12 + 15
= 120 + 15
= 135
(b)
Number of black beads
= 9 u
= 9 x 12
= 108
Fraction of Hilda's beads that is black
=
108135=
45 Answer(s): (a) 135; (b)
45 
