Jane had some brown and white balls. If she gives away 21 brown balls, the number of brown balls will be 10% of the total number of balls left. If she gives away 45 white balls, the number of brown balls will be 25% of the total number of balls left.
- How many balls does Jane have altogether?
- What fraction of Jane's balls is white?
| |
Scenario 1 |
Scenario 2 |
| |
Brown |
White |
Brown |
White |
| Before |
1 u + 21 |
9 u |
1 p |
3 p + 45 |
| Change |
- 21 |
No change |
No change |
- 45 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 21 = 1 p --- (1)
9 u = 3 p + 45
9 u - 45 = 3 p --- (2)
Make p the same.
(1)
x33 u + 63 = 3 p --- (3)
(2) = (3)
9 u - 45 = 3 u + 63
9 u - 3 u = 63 + 45
6 u = 108
1 u = 108 ÷ 6 = 18
Number of balls that Jane had at first
= 1 u + 21 + 9 u
= 10 u + 21
= 10 x 18 + 21
= 180 + 21
= 201
(b)
Number of white balls
= 9 u
= 9 x 18
= 162
Fraction of Jane's balls that is white
=
162201=
5467 Answer(s): (a) 201; (b)
5467 
