Diana had some gold and blue balls. If she gives away 11 gold balls, the number of gold balls will be 20% of the total number of balls left. If she gives away 16 blue balls, the number of gold balls will be 25% of the total number of balls left.
- How many balls does Diana have altogether?
- What fraction of Diana's balls is blue?
| |
Scenario 1 |
Scenario 2 |
| |
Gold |
Blue |
Gold |
Blue |
| Before |
1 u + 11 |
4 u |
1 p |
3 p + 16 |
| Change |
- 11 |
No change |
No change |
- 16 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 11 = 1 p --- (1)
4 u = 3 p + 16
4 u - 16 = 3 p --- (2)
Make p the same.
(1)
x33 u + 33 = 3 p --- (3)
(2) = (3)
4 u - 16 = 3 u + 33
4 u - 3 u = 33 + 16
1 u = 49
Number of balls that Diana had at first
= 1 u + 11 + 4 u
= 5 u + 11
= 5 x 49 + 11
= 245 + 11
= 256
(b)
Number of blue balls
= 4 u
= 4 x 49
= 196
Fraction of Diana's balls that is blue
=
196256=
4964 Answer(s): (a) 256; (b)
4964 
