Kimberly had some pink and brown balls. If she gives away 40 pink balls, the number of pink balls will be 10% of the total number of balls left. If she gives away 18 brown balls, the number of pink balls will be 25% of the total number of balls left.
- How many balls does Kimberly have altogether?
- What fraction of Kimberly's balls is brown?
|
Scenario 1 |
Scenario 2 |
|
Pink |
Brown |
Pink |
Brown |
Before |
1 u + 40 |
9 u |
1 p |
3 p + 18 |
Change |
- 40 |
No change |
No change |
- 18 |
After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 40 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 120 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 120
9 u - 3 u = 120 + 18
6 u = 138
1 u = 138 ÷ 6 = 23
Number of balls that Kimberly had at first
= 1 u + 40 + 9 u
= 10 u + 40
= 10 x 23 + 40
= 230 + 40
= 270
(b)
Number of brown balls
= 9 u
= 9 x 23
= 207
Fraction of Kimberly's balls that is brown
=
207270=
2330 Answer(s): (a) 270; (b)
2330