Opal had some purple and grey balls. If she gives away 15 purple balls, the number of purple balls will be 20% of the total number of balls left. If she gives away 35 grey balls, the number of purple balls will be 25% of the total number of balls left.
- How many balls does Opal have altogether?
- What fraction of Opal's balls is grey?
| |
Scenario 1 |
Scenario 2 |
| |
Purple |
Grey |
Purple |
Grey |
| Before |
1 u + 15 |
4 u |
1 p |
3 p + 35 |
| Change |
- 15 |
No change |
No change |
- 35 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 15 = 1 p --- (1)
4 u = 3 p + 35
4 u - 35 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
4 u - 35 = 3 u + 45
4 u - 3 u = 45 + 35
1 u = 80
Number of balls that Opal had at first
= 1 u + 15 + 4 u
= 5 u + 15
= 5 x 80 + 15
= 400 + 15
= 415
(b)
Number of grey balls
= 4 u
= 4 x 80
= 320
Fraction of Opal's balls that is grey
=
320415=
6483 Answer(s): (a) 415; (b)
6483 
