Dana had some purple and brown marbles. If she gives away 13 purple marbles, the number of purple marbles will be 20% of the total number of marbles left. If she gives away 12 brown marbles, the number of purple marbles will be 25% of the total number of marbles left.
- How many marbles does Dana have altogether?
- What fraction of Dana's marbles is brown?
| |
Scenario 1 |
Scenario 2 |
| |
Purple |
Brown |
Purple |
Brown |
| Before |
1 u + 13 |
4 u |
1 p |
3 p + 12 |
| Change |
- 13 |
No change |
No change |
- 12 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 13 = 1 p --- (1)
4 u = 3 p + 12
4 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 39 = 3 p --- (3)
(2) = (3)
4 u - 12 = 3 u + 39
4 u - 3 u = 39 + 12
1 u = 51
Number of marbles that Dana had at first
= 1 u + 13 + 4 u
= 5 u + 13
= 5 x 51 + 13
= 255 + 13
= 268
(b)
Number of brown marbles
= 4 u
= 4 x 51
= 204
Fraction of Dana's marbles that is brown
=
204268=
5167 Answer(s): (a) 268; (b)
5167 
