Tammy had some red and black marbles. If she gives away 11 red marbles, the number of red marbles will be 20% of the total number of marbles left. If she gives away 40 black marbles, the number of red marbles will be 25% of the total number of marbles left.
- How many marbles does Tammy have altogether?
- What fraction of Tammy's marbles is black?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Black |
Red |
Black |
| Before |
1 u + 11 |
4 u |
1 p |
3 p + 40 |
| Change |
- 11 |
No change |
No change |
- 40 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 11 = 1 p --- (1)
4 u = 3 p + 40
4 u - 40 = 3 p --- (2)
Make p the same.
(1)
x33 u + 33 = 3 p --- (3)
(2) = (3)
4 u - 40 = 3 u + 33
4 u - 3 u = 33 + 40
1 u = 73
Number of marbles that Tammy had at first
= 1 u + 11 + 4 u
= 5 u + 11
= 5 x 73 + 11
= 365 + 11
= 376
(b)
Number of black marbles
= 4 u
= 4 x 73
= 292
Fraction of Tammy's marbles that is black
=
292376=
7394 Answer(s): (a) 376; (b)
7394 
