Yen had some white and gold balls. If she gives away 14 white balls, the number of white balls will be 10% of the total number of balls left. If she gives away 30 gold balls, the number of white balls will be 25% of the total number of balls left.
- How many balls does Yen have altogether?
- What fraction of Yen's balls is gold?
| |
Scenario 1 |
Scenario 2 |
| |
White |
Gold |
White |
Gold |
| Before |
1 u + 14 |
9 u |
1 p |
3 p + 30 |
| Change |
- 14 |
No change |
No change |
- 30 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 14 = 1 p --- (1)
9 u = 3 p + 30
9 u - 30 = 3 p --- (2)
Make p the same.
(1)
x33 u + 42 = 3 p --- (3)
(2) = (3)
9 u - 30 = 3 u + 42
9 u - 3 u = 42 + 30
6 u = 72
1 u = 72 ÷ 6 = 12
Number of balls that Yen had at first
= 1 u + 14 + 9 u
= 10 u + 14
= 10 x 12 + 14
= 120 + 14
= 134
(b)
Number of gold balls
= 9 u
= 9 x 12
= 108
Fraction of Yen's balls that is gold
=
108134=
5467 Answer(s): (a) 134; (b)
5467 
