Zara had some gold and silver beads. If she gives away 30 gold beads, the number of gold beads will be 10% of the total number of beads left. If she gives away 30 silver beads, the number of gold beads will be 25% of the total number of beads left.
- How many beads does Zara have altogether?
- What fraction of Zara's beads is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Silver |
Gold |
Silver |
| Before |
1 u + 30 |
9 u |
1 p |
3 p + 30 |
| Change |
- 30 |
No change |
No change |
- 30 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 30 = 1 p --- (1)
9 u = 3 p + 30
9 u - 30 = 3 p --- (2)
Make p the same.
(1)
x33 u + 90 = 3 p --- (3)
(2) = (3)
9 u - 30 = 3 u + 90
9 u - 3 u = 90 + 30
6 u = 120
1 u = 120 ÷ 6 = 20
Number of beads that Zara had at first
= 1 u + 30 + 9 u
= 10 u + 30
= 10 x 20 + 30
= 200 + 30
= 230
(b)
Number of silver beads
= 9 u
= 9 x 20
= 180
Fraction of Zara's beads that is silver
=
180230=
1823 Answer(s): (a) 230; (b)
1823 
