Pamela had some blue and gold beads. If she gives away 18 blue beads, the number of blue beads will be 10% of the total number of beads left. If she gives away 36 gold beads, the number of blue beads will be 25% of the total number of beads left.
- How many beads does Pamela have altogether?
- What fraction of Pamela's beads is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Blue |
Gold |
Blue |
Gold |
| Before |
1 u + 18 |
9 u |
1 p |
3 p + 36 |
| Change |
- 18 |
No change |
No change |
- 36 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 18 = 1 p --- (1)
9 u = 3 p + 36
9 u - 36 = 3 p --- (2)
Make p the same.
(1)
x33 u + 54 = 3 p --- (3)
(2) = (3)
9 u - 36 = 3 u + 54
9 u - 3 u = 54 + 36
6 u = 90
1 u = 90 ÷ 6 = 15
Number of beads that Pamela had at first
= 1 u + 18 + 9 u
= 10 u + 18
= 10 x 15 + 18
= 150 + 18
= 168
(b)
Number of gold beads
= 9 u
= 9 x 15
= 135
Fraction of Pamela's beads that is gold
=
135168=
4556 Answer(s): (a) 168; (b)
4556 
