Gwen had some grey and green balls. If she gives away 19 grey balls, the number of grey balls will be 20% of the total number of balls left. If she gives away 19 green balls, the number of grey balls will be 25% of the total number of balls left.
- How many balls does Gwen have altogether?
- What fraction of Gwen's balls is green?
| |
Scenario 1 |
Scenario 2 |
| |
Grey |
Green |
Grey |
Green |
| Before |
1 u + 19 |
4 u |
1 p |
3 p + 19 |
| Change |
- 19 |
No change |
No change |
- 19 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 19 = 1 p --- (1)
4 u = 3 p + 19
4 u - 19 = 3 p --- (2)
Make p the same.
(1)
x33 u + 57 = 3 p --- (3)
(2) = (3)
4 u - 19 = 3 u + 57
4 u - 3 u = 57 + 19
1 u = 76
Number of balls that Gwen had at first
= 1 u + 19 + 4 u
= 5 u + 19
= 5 x 76 + 19
= 380 + 19
= 399
(b)
Number of green balls
= 4 u
= 4 x 76
= 304
Fraction of Gwen's balls that is green
=
304399=
1621 Answer(s): (a) 399; (b)
1621 
