Cathy had some yellow and grey beads. If she gives away 28 yellow beads, the number of yellow beads will be 20% of the total number of beads left. If she gives away 16 grey beads, the number of yellow beads will be 25% of the total number of beads left.
- How many beads does Cathy have altogether?
- What fraction of Cathy's beads is grey?
|
Scenario 1 |
Scenario 2 |
|
Yellow |
Grey |
Yellow |
Grey |
Before |
1 u + 28 |
4 u |
1 p |
3 p + 16 |
Change |
- 28 |
No change |
No change |
- 16 |
After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 28 = 1 p --- (1)
4 u = 3 p + 16
4 u - 16 = 3 p --- (2)
Make p the same.
(1)
x33 u + 84 = 3 p --- (3)
(2) = (3)
4 u - 16 = 3 u + 84
4 u - 3 u = 84 + 16
1 u = 100
Number of beads that Cathy had at first
= 1 u + 28 + 4 u
= 5 u + 28
= 5 x 100 + 28
= 500 + 28
= 528
(b)
Number of grey beads
= 4 u
= 4 x 100
= 400
Fraction of Cathy's beads that is grey
=
400528=
2533 Answer(s): (a) 528; (b)
2533