Tina had some red and pink marbles. If she gives away 18 red marbles, the number of red marbles will be 20% of the total number of marbles left. If she gives away 27 pink marbles, the number of red marbles will be 25% of the total number of marbles left.
- How many marbles does Tina have altogether?
- What fraction of Tina's marbles is pink?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Pink |
Red |
Pink |
| Before |
1 u + 18 |
4 u |
1 p |
3 p + 27 |
| Change |
- 18 |
No change |
No change |
- 27 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 18 = 1 p --- (1)
4 u = 3 p + 27
4 u - 27 = 3 p --- (2)
Make p the same.
(1)
x33 u + 54 = 3 p --- (3)
(2) = (3)
4 u - 27 = 3 u + 54
4 u - 3 u = 54 + 27
1 u = 81
Number of marbles that Tina had at first
= 1 u + 18 + 4 u
= 5 u + 18
= 5 x 81 + 18
= 405 + 18
= 423
(b)
Number of pink marbles
= 4 u
= 4 x 81
= 324
Fraction of Tina's marbles that is pink
=
324423=
3647 Answer(s): (a) 423; (b)
3647 
