Victoria had some silver and white balls. If she gives away 14 silver balls, the number of silver balls will be 20% of the total number of balls left. If she gives away 14 white balls, the number of silver balls will be 25% of the total number of balls left.
- How many balls does Victoria have altogether?
- What fraction of Victoria's balls is white?
| |
Scenario 1 |
Scenario 2 |
| |
Silver |
White |
Silver |
White |
| Before |
1 u + 14 |
4 u |
1 p |
3 p + 14 |
| Change |
- 14 |
No change |
No change |
- 14 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 14 = 1 p --- (1)
4 u = 3 p + 14
4 u - 14 = 3 p --- (2)
Make p the same.
(1)
x33 u + 42 = 3 p --- (3)
(2) = (3)
4 u - 14 = 3 u + 42
4 u - 3 u = 42 + 14
1 u = 56
Number of balls that Victoria had at first
= 1 u + 14 + 4 u
= 5 u + 14
= 5 x 56 + 14
= 280 + 14
= 294
(b)
Number of white balls
= 4 u
= 4 x 56
= 224
Fraction of Victoria's balls that is white
=
224294=
1621 Answer(s): (a) 294; (b)
1621 
