Wendy had some black and gold balls. If she gives away 16 black balls, the number of black balls will be 10% of the total number of balls left. If she gives away 48 gold balls, the number of black balls will be 25% of the total number of balls left.
- How many balls does Wendy have altogether?
- What fraction of Wendy's balls is gold?
| |
Scenario 1 |
Scenario 2 |
| |
Black |
Gold |
Black |
Gold |
| Before |
1 u + 16 |
9 u |
1 p |
3 p + 48 |
| Change |
- 16 |
No change |
No change |
- 48 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 16 = 1 p --- (1)
9 u = 3 p + 48
9 u - 48 = 3 p --- (2)
Make p the same.
(1)
x33 u + 48 = 3 p --- (3)
(2) = (3)
9 u - 48 = 3 u + 48
9 u - 3 u = 48 + 48
6 u = 96
1 u = 96 ÷ 6 = 16
Number of balls that Wendy had at first
= 1 u + 16 + 9 u
= 10 u + 16
= 10 x 16 + 16
= 160 + 16
= 176
(b)
Number of gold balls
= 9 u
= 9 x 16
= 144
Fraction of Wendy's balls that is gold
=
144176=
911 Answer(s): (a) 176; (b)
911 
