Shannon had some gold and grey balls. If she gives away 45 gold balls, the number of gold balls will be 10% of the total number of balls left. If she gives away 15 grey balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Shannon have altogether?
- What fraction of Shannon's balls is grey?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Grey |
Gold |
Grey |
| Before |
1 u + 45 |
9 u |
1 p |
3 p + 15 |
| Change |
- 45 |
No change |
No change |
- 15 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 45 = 1 p --- (1)
9 u = 3 p + 15
9 u - 15 = 3 p --- (2)
Make p the same.
(1)
x33 u + 135 = 3 p --- (3)
(2) = (3)
9 u - 15 = 3 u + 135
9 u - 3 u = 135 + 15
6 u = 150
1 u = 150 ÷ 6 = 25
Number of balls that Shannon had at first
= 1 u + 45 + 9 u
= 10 u + 45
= 10 x 25 + 45
= 250 + 45
= 295
(b)
Number of grey balls
= 9 u
= 9 x 25
= 225
Fraction of Shannon's balls that is grey
=
225295=
4559 Answer(s): (a) 295; (b)
4559 
