Lynn had some purple and silver balls. If she gives away 30 purple balls, the number of purple balls will be 20% of the total number of balls left. If she gives away 45 silver balls, the number of purple balls will be 25% of the total number of balls left.
- How many balls does Lynn have altogether?
- What fraction of Lynn's balls is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Purple |
Silver |
Purple |
Silver |
| Before |
1 u + 30 |
4 u |
1 p |
3 p + 45 |
| Change |
- 30 |
No change |
No change |
- 45 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 30 = 1 p --- (1)
4 u = 3 p + 45
4 u - 45 = 3 p --- (2)
Make p the same.
(1)
x33 u + 90 = 3 p --- (3)
(2) = (3)
4 u - 45 = 3 u + 90
4 u - 3 u = 90 + 45
1 u = 135
Number of balls that Lynn had at first
= 1 u + 30 + 4 u
= 5 u + 30
= 5 x 135 + 30
= 675 + 30
= 705
(b)
Number of silver balls
= 4 u
= 4 x 135
= 540
Fraction of Lynn's balls that is silver
=
540705=
3647 Answer(s): (a) 705; (b)
3647 
