Rachel had some grey and gold marbles. If she gives away 16 grey marbles, the number of grey marbles will be 10% of the total number of marbles left. If she gives away 24 gold marbles, the number of grey marbles will be 25% of the total number of marbles left.
- How many marbles does Rachel have altogether?
- What fraction of Rachel's marbles is gold?
|
Scenario 1 |
Scenario 2 |
|
Grey |
Gold |
Grey |
Gold |
Before |
1 u + 16 |
9 u |
1 p |
3 p + 24 |
Change |
- 16 |
No change |
No change |
- 24 |
After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 16 = 1 p --- (1)
9 u = 3 p + 24
9 u - 24 = 3 p --- (2)
Make p the same.
(1)
x33 u + 48 = 3 p --- (3)
(2) = (3)
9 u - 24 = 3 u + 48
9 u - 3 u = 48 + 24
6 u = 72
1 u = 72 ÷ 6 = 12
Number of marbles that Rachel had at first
= 1 u + 16 + 9 u
= 10 u + 16
= 10 x 12 + 16
= 120 + 16
= 136
(b)
Number of gold marbles
= 9 u
= 9 x 12
= 108
Fraction of Rachel's marbles that is gold
=
108136=
2734 Answer(s): (a) 136; (b)
2734