Zoe had some yellow and red beads. If she gives away 24 yellow beads, the number of yellow beads will be 20% of the total number of beads left. If she gives away 40 red beads, the number of yellow beads will be 25% of the total number of beads left.
- How many beads does Zoe have altogether?
- What fraction of Zoe's beads is red?
| |
Scenario 1 |
Scenario 2 |
| |
Yellow |
Red |
Yellow |
Red |
| Before |
1 u + 24 |
4 u |
1 p |
3 p + 40 |
| Change |
- 24 |
No change |
No change |
- 40 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 24 = 1 p --- (1)
4 u = 3 p + 40
4 u - 40 = 3 p --- (2)
Make p the same.
(1)
x33 u + 72 = 3 p --- (3)
(2) = (3)
4 u - 40 = 3 u + 72
4 u - 3 u = 72 + 40
1 u = 112
Number of beads that Zoe had at first
= 1 u + 24 + 4 u
= 5 u + 24
= 5 x 112 + 24
= 560 + 24
= 584
(b)
Number of red beads
= 4 u
= 4 x 112
= 448
Fraction of Zoe's beads that is red
=
448584=
5673 Answer(s): (a) 584; (b)
5673 
