Shiyun had some grey and brown marbles. If she gives away 12 grey marbles, the number of grey marbles will be 20% of the total number of marbles left. If she gives away 18 brown marbles, the number of grey marbles will be 25% of the total number of marbles left.
- How many marbles does Shiyun have altogether?
- What fraction of Shiyun's marbles is brown?
| |
Scenario 1 |
Scenario 2 |
| |
Grey |
Brown |
Grey |
Brown |
| Before |
1 u + 12 |
4 u |
1 p |
3 p + 18 |
| Change |
- 12 |
No change |
No change |
- 18 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 12 = 1 p --- (1)
4 u = 3 p + 18
4 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 36 = 3 p --- (3)
(2) = (3)
4 u - 18 = 3 u + 36
4 u - 3 u = 36 + 18
1 u = 54
Number of marbles that Shiyun had at first
= 1 u + 12 + 4 u
= 5 u + 12
= 5 x 54 + 12
= 270 + 12
= 282
(b)
Number of brown marbles
= 4 u
= 4 x 54
= 216
Fraction of Shiyun's marbles that is brown
=
216282=
3647 Answer(s): (a) 282; (b)
3647 
