Zara had some gold and black beads. If she gives away 15 gold beads, the number of gold beads will be 20% of the total number of beads left. If she gives away 15 black 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 black?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Black |
Gold |
Black |
| Before |
1 u + 15 |
4 u |
1 p |
3 p + 15 |
| Change |
- 15 |
No change |
No change |
- 15 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 15 = 1 p --- (1)
4 u = 3 p + 15
4 u - 15 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
4 u - 15 = 3 u + 45
4 u - 3 u = 45 + 15
1 u = 60
Number of beads that Zara had at first
= 1 u + 15 + 4 u
= 5 u + 15
= 5 x 60 + 15
= 300 + 15
= 315
(b)
Number of black beads
= 4 u
= 4 x 60
= 240
Fraction of Zara's beads that is black
=
240315=
1621 Answer(s): (a) 315; (b)
1621 
