Hazel had some yellow and white balls. If she gives away 16 yellow balls, the number of yellow balls will be 20% of the total number of balls left. If she gives away 12 white balls, the number of yellow balls will be 25% of the total number of balls left.
- How many balls does Hazel have altogether?
- What fraction of Hazel's balls is white?
| |
Scenario 1 |
Scenario 2 |
| |
Yellow |
White |
Yellow |
White |
| Before |
1 u + 16 |
4 u |
1 p |
3 p + 12 |
| Change |
- 16 |
No change |
No change |
- 12 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 16 = 1 p --- (1)
4 u = 3 p + 12
4 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 48 = 3 p --- (3)
(2) = (3)
4 u - 12 = 3 u + 48
4 u - 3 u = 48 + 12
1 u = 60
Number of balls that Hazel had at first
= 1 u + 16 + 4 u
= 5 u + 16
= 5 x 60 + 16
= 300 + 16
= 316
(b)
Number of white balls
= 4 u
= 4 x 60
= 240
Fraction of Hazel's balls that is white
=
240316=
6079 Answer(s): (a) 316; (b)
6079 
