Dana had some green and brown balls. If she gives away 15 green balls, the number of green balls will be 10% of the total number of balls left. If she gives away 45 brown balls, the number of green balls will be 25% of the total number of balls left.
- How many balls does Dana have altogether?
- What fraction of Dana's balls is brown?
| |
Scenario 1 |
Scenario 2 |
| |
Green |
Brown |
Green |
Brown |
| Before |
1 u + 15 |
9 u |
1 p |
3 p + 45 |
| Change |
- 15 |
No change |
No change |
- 45 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 15 = 1 p --- (1)
9 u = 3 p + 45
9 u - 45 = 3 p --- (2)
Make p the same.
(1)
x33 u + 45 = 3 p --- (3)
(2) = (3)
9 u - 45 = 3 u + 45
9 u - 3 u = 45 + 45
6 u = 90
1 u = 90 ÷ 6 = 15
Number of balls that Dana had at first
= 1 u + 15 + 9 u
= 10 u + 15
= 10 x 15 + 15
= 150 + 15
= 165
(b)
Number of brown balls
= 9 u
= 9 x 15
= 135
Fraction of Dana's balls that is brown
=
135165=
911 Answer(s): (a) 165; (b)
911 
