Usha had some red and black marbles. If she gives away 28 red marbles, the number of red marbles will be 10% of the total number of marbles left. If she gives away 12 black marbles, the number of red marbles will be 25% of the total number of marbles left.
- How many marbles does Usha have altogether?
- What fraction of Usha's marbles is black?
|
Scenario 1 |
Scenario 2 |
|
Red |
Black |
Red |
Black |
Before |
1 u + 28 |
9 u |
1 p |
3 p + 12 |
Change |
- 28 |
No change |
No change |
- 12 |
After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 28 = 1 p --- (1)
9 u = 3 p + 12
9 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 84 = 3 p --- (3)
(2) = (3)
9 u - 12 = 3 u + 84
9 u - 3 u = 84 + 12
6 u = 96
1 u = 96 ÷ 6 = 16
Number of marbles that Usha had at first
= 1 u + 28 + 9 u
= 10 u + 28
= 10 x 16 + 28
= 160 + 28
= 188
(b)
Number of black marbles
= 9 u
= 9 x 16
= 144
Fraction of Usha's marbles that is black
=
144188=
3647 Answer(s): (a) 188; (b)
3647