Sarah had some brown and black balls. If she gives away 35 brown balls, the number of brown balls will be 10% of the total number of balls left. If she gives away 15 black balls, the number of brown balls will be 25% of the total number of balls left.
- How many balls does Sarah have altogether?
- What fraction of Sarah's balls is black?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
Black |
Brown |
Black |
| Before |
1 u + 35 |
9 u |
1 p |
3 p + 15 |
| Change |
- 35 |
No change |
No change |
- 15 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 35 = 1 p --- (1)
9 u = 3 p + 15
9 u - 15 = 3 p --- (2)
Make p the same.
(1)
x33 u + 105 = 3 p --- (3)
(2) = (3)
9 u - 15 = 3 u + 105
9 u - 3 u = 105 + 15
6 u = 120
1 u = 120 ÷ 6 = 20
Number of balls that Sarah had at first
= 1 u + 35 + 9 u
= 10 u + 35
= 10 x 20 + 35
= 200 + 35
= 235
(b)
Number of black balls
= 9 u
= 9 x 20
= 180
Fraction of Sarah's balls that is black
=
180235=
3647 Answer(s): (a) 235; (b)
3647 
