Emma had some gold and black balls. If she gives away 28 gold balls, the number of gold balls will be 10% of the total number of balls left. If she gives away 42 black balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Emma have altogether?
- What fraction of Emma's balls is black?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Black |
Gold |
Black |
| Before |
1 u + 28 |
9 u |
1 p |
3 p + 42 |
| Change |
- 28 |
No change |
No change |
- 42 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 28 = 1 p --- (1)
9 u = 3 p + 42
9 u - 42 = 3 p --- (2)
Make p the same.
(1)
x33 u + 84 = 3 p --- (3)
(2) = (3)
9 u - 42 = 3 u + 84
9 u - 3 u = 84 + 42
6 u = 126
1 u = 126 ÷ 6 = 21
Number of balls that Emma had at first
= 1 u + 28 + 9 u
= 10 u + 28
= 10 x 21 + 28
= 210 + 28
= 238
(b)
Number of black balls
= 9 u
= 9 x 21
= 189
Fraction of Emma's balls that is black
=
189238=
2734 Answer(s): (a) 238; (b)
2734 
