Zara had some silver and purple marbles. If she gives away 20 silver marbles, the number of silver marbles will be 20% of the total number of marbles left. If she gives away 24 purple marbles, the number of silver marbles will be 25% of the total number of marbles left.
- How many marbles does Zara have altogether?
- What fraction of Zara's marbles is purple?
|
Scenario 1 |
Scenario 2 |
|
Silver |
Purple |
Silver |
Purple |
Before |
1 u + 20 |
4 u |
1 p |
3 p + 24 |
Change |
- 20 |
No change |
No change |
- 24 |
After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 20 = 1 p --- (1)
4 u = 3 p + 24
4 u - 24 = 3 p --- (2)
Make p the same.
(1)
x33 u + 60 = 3 p --- (3)
(2) = (3)
4 u - 24 = 3 u + 60
4 u - 3 u = 60 + 24
1 u = 84
Number of marbles that Zara had at first
= 1 u + 20 + 4 u
= 5 u + 20
= 5 x 84 + 20
= 420 + 20
= 440
(b)
Number of purple marbles
= 4 u
= 4 x 84
= 336
Fraction of Zara's marbles that is purple
=
336440=
4255 Answer(s): (a) 440; (b)
4255