Tina had some black and gold marbles. If she gives away 13 black marbles, the number of black marbles will be 10% of the total number of marbles left. If she gives away 45 gold marbles, the number of black marbles will be 25% of the total number of marbles left.
- How many marbles does Tina have altogether?
- What fraction of Tina's marbles is gold?
|
Scenario 1 |
Scenario 2 |
|
Black |
Gold |
Black |
Gold |
Before |
1 u + 13 |
9 u |
1 p |
3 p + 45 |
Change |
- 13 |
No change |
No change |
- 45 |
After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 13 = 1 p --- (1)
9 u = 3 p + 45
9 u - 45 = 3 p --- (2)
Make p the same.
(1)
x33 u + 39 = 3 p --- (3)
(2) = (3)
9 u - 45 = 3 u + 39
9 u - 3 u = 39 + 45
6 u = 84
1 u = 84 ÷ 6 = 14
Number of marbles that Tina had at first
= 1 u + 13 + 9 u
= 10 u + 13
= 10 x 14 + 13
= 140 + 13
= 153
(b)
Number of gold marbles
= 9 u
= 9 x 14
= 126
Fraction of Tina's marbles that is gold
=
126153=
1417 Answer(s): (a) 153; (b)
1417