Jaslyn had some gold and black beads. If she gives away 24 gold beads, the number of gold beads will be 20% of the total number of beads left. If she gives away 32 black beads, the number of gold beads will be 25% of the total number of beads left.
- How many beads does Jaslyn have altogether?
- What fraction of Jaslyn's beads is black?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Black |
Gold |
Black |
| Before |
1 u + 24 |
4 u |
1 p |
3 p + 32 |
| Change |
- 24 |
No change |
No change |
- 32 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 24 = 1 p --- (1)
4 u = 3 p + 32
4 u - 32 = 3 p --- (2)
Make p the same.
(1)
x33 u + 72 = 3 p --- (3)
(2) = (3)
4 u - 32 = 3 u + 72
4 u - 3 u = 72 + 32
1 u = 104
Number of beads that Jaslyn had at first
= 1 u + 24 + 4 u
= 5 u + 24
= 5 x 104 + 24
= 520 + 24
= 544
(b)
Number of black beads
= 4 u
= 4 x 104
= 416
Fraction of Jaslyn's beads that is black
=
416544=
1317 Answer(s): (a) 544; (b)
1317 
