Nicole had some gold and silver balls. If she gives away 22 gold balls, the number of gold balls will be 10% of the total number of balls left. If she gives away 18 silver balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Nicole have altogether?
- What fraction of Nicole's balls is silver?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Silver |
Gold |
Silver |
| Before |
1 u + 22 |
9 u |
1 p |
3 p + 18 |
| Change |
- 22 |
No change |
No change |
- 18 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 22 = 1 p --- (1)
9 u = 3 p + 18
9 u - 18 = 3 p --- (2)
Make p the same.
(1)
x33 u + 66 = 3 p --- (3)
(2) = (3)
9 u - 18 = 3 u + 66
9 u - 3 u = 66 + 18
6 u = 84
1 u = 84 ÷ 6 = 14
Number of balls that Nicole had at first
= 1 u + 22 + 9 u
= 10 u + 22
= 10 x 14 + 22
= 140 + 22
= 162
(b)
Number of silver balls
= 9 u
= 9 x 14
= 126
Fraction of Nicole's balls that is silver
=
126162=
79 Answer(s): (a) 162; (b)
79 
