Irene had some gold and green balls. If she gives away 15 gold balls, the number of gold balls will be 20% of the total number of balls left. If she gives away 10 green balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Irene have altogether?
- What fraction of Irene's balls is green?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Green |
Gold |
Green |
| Before |
1 u + 15 |
4 u |
1 p |
3 p + 10 |
| Change |
- 15 |
No change |
No change |
- 10 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 15 = 1 p --- (1)
4 u = 3 p + 10
4 u - 10 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
4 u - 10 = 3 u + 45
4 u - 3 u = 45 + 10
1 u = 55
Number of balls that Irene had at first
= 1 u + 15 + 4 u
= 5 u + 15
= 5 x 55 + 15
= 275 + 15
= 290
(b)
Number of green balls
= 4 u
= 4 x 55
= 220
Fraction of Irene's balls that is green
=
220290=
2229 Answer(s): (a) 290; (b)
2229 
