Dana had some green and yellow beads. If she gives away 16 green beads, the number of green beads will be 20% of the total number of beads left. If she gives away 24 yellow beads, the number of green beads will be 25% of the total number of beads left.
- How many beads does Dana have altogether?
- What fraction of Dana's beads is yellow?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Yellow |
Green |
Yellow |
| Before |
1 u + 16 |
4 u |
1 p |
3 p + 24 |
| Change |
- 16 |
No change |
No change |
- 24 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 16 = 1 p --- (1)
4 u = 3 p + 24
4 u - 24 = 3 p --- (2)
Make p the same.
(1)
x33 u + 48 = 3 p --- (3)
(2) = (3)
4 u - 24 = 3 u + 48
4 u - 3 u = 48 + 24
1 u = 72
Number of beads that Dana had at first
= 1 u + 16 + 4 u
= 5 u + 16
= 5 x 72 + 16
= 360 + 16
= 376
(b)
Number of yellow beads
= 4 u
= 4 x 72
= 288
Fraction of Dana's beads that is yellow
=
288376=
3647 Answer(s): (a) 376; (b)
3647 
