Fanny had some brown and pink beads. If she gives away 50 brown beads, the number of brown beads will be 20% of the total number of beads left. If she gives away 25 pink beads, the number of brown beads will be 25% of the total number of beads left.
- How many beads does Fanny have altogether?
- What fraction of Fanny's beads is pink?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Pink |
Brown |
Pink |
| Before |
1 u + 50 |
4 u |
1 p |
3 p + 25 |
| Change |
- 50 |
No change |
No change |
- 25 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 50 = 1 p --- (1)
4 u = 3 p + 25
4 u - 25 = 3 p --- (2)
Make p the same.
(1)
x33 u + 150 = 3 p --- (3)
(2) = (3)
4 u - 25 = 3 u + 150
4 u - 3 u = 150 + 25
1 u = 175
Number of beads that Fanny had at first
= 1 u + 50 + 4 u
= 5 u + 50
= 5 x 175 + 50
= 875 + 50
= 925
(b)
Number of pink beads
= 4 u
= 4 x 175
= 700
Fraction of Fanny's beads that is pink
=
700925=
2837 Answer(s): (a) 925; (b)
2837 
