Fanny had some silver and pink marbles. If she gives away 10 silver marbles, the number of silver marbles will be 20% of the total number of marbles left. If she gives away 12 pink marbles, the number of silver marbles will be 25% of the total number of marbles left.
- How many marbles does Fanny have altogether?
- What fraction of Fanny's marbles is pink?
| |
Scenario 1 |
Scenario 2 |
| |
Silver |
Pink |
Silver |
Pink |
| Before |
1 u + 10 |
4 u |
1 p |
3 p + 12 |
| Change |
- 10 |
No change |
No change |
- 12 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 10 = 1 p --- (1)
4 u = 3 p + 12
4 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 30 = 3 p --- (3)
(2) = (3)
4 u - 12 = 3 u + 30
4 u - 3 u = 30 + 12
1 u = 42
Number of marbles that Fanny had at first
= 1 u + 10 + 4 u
= 5 u + 10
= 5 x 42 + 10
= 210 + 10
= 220
(b)
Number of pink marbles
= 4 u
= 4 x 42
= 168
Fraction of Fanny's marbles that is pink
=
168220=
4255 Answer(s): (a) 220; (b)
4255 
