Gem had some grey and blue marbles. If she gives away 27 grey marbles, the number of grey marbles will be 20% of the total number of marbles left. If she gives away 30 blue marbles, the number of grey marbles will be 25% of the total number of marbles left.
- How many marbles does Gem have altogether?
- What fraction of Gem's marbles is blue?
| |
Scenario 1 |
Scenario 2 |
| |
Grey |
Blue |
Grey |
Blue |
| Before |
1 u + 27 |
4 u |
1 p |
3 p + 30 |
| Change |
- 27 |
No change |
No change |
- 30 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 27 = 1 p --- (1)
4 u = 3 p + 30
4 u - 30 = 3 p --- (2)
Make p the same.
(1)
x33 u + 81 = 3 p --- (3)
(2) = (3)
4 u - 30 = 3 u + 81
4 u - 3 u = 81 + 30
1 u = 111
Number of marbles that Gem had at first
= 1 u + 27 + 4 u
= 5 u + 27
= 5 x 111 + 27
= 555 + 27
= 582
(b)
Number of blue marbles
= 4 u
= 4 x 111
= 444
Fraction of Gem's marbles that is blue
=
444582=
7497 Answer(s): (a) 582; (b)
7497 
