Gabby had some black and red marbles. If she gives away 43 black marbles, the number of black marbles will be 20% of the total number of marbles left. If she gives away 43 red marbles, the number of black marbles will be 25% of the total number of marbles left.
- How many marbles does Gabby have altogether?
- What fraction of Gabby's marbles is red?
| |
Scenario 1 |
Scenario 2 |
| |
Black |
Red |
Black |
Red |
| Before |
1 u + 43 |
4 u |
1 p |
3 p + 43 |
| Change |
- 43 |
No change |
No change |
- 43 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 43 = 1 p --- (1)
4 u = 3 p + 43
4 u - 43 = 3 p --- (2)
Make p the same.
(1)
x33 u + 129 = 3 p --- (3)
(2) = (3)
4 u - 43 = 3 u + 129
4 u - 3 u = 129 + 43
1 u = 172
Number of marbles that Gabby had at first
= 1 u + 43 + 4 u
= 5 u + 43
= 5 x 172 + 43
= 860 + 43
= 903
(b)
Number of red marbles
= 4 u
= 4 x 172
= 688
Fraction of Gabby's marbles that is red
=
688903=
1621 Answer(s): (a) 903; (b)
1621 
