Cindy had some red and blue balls. If she gives away 29 red balls, the number of red balls will be 10% of the total number of balls left. If she gives away 27 blue balls, the number of red balls will be 25% of the total number of balls left.
- How many balls does Cindy have altogether?
- What fraction of Cindy's balls is blue?
| |
Scenario 1 |
Scenario 2 |
| |
Red |
Blue |
Red |
Blue |
| Before |
1 u + 29 |
9 u |
1 p |
3 p + 27 |
| Change |
- 29 |
No change |
No change |
- 27 |
| After |
1 u |
9 u |
1 p |
3 p |
(a)
10% =
10100 =
11025% =
25100 =
141 u + 29 = 1 p --- (1)
9 u = 3 p + 27
9 u - 27 = 3 p --- (2)
Make p the same.
(1)
x33 u + 87 = 3 p --- (3)
(2) = (3)
9 u - 27 = 3 u + 87
9 u - 3 u = 87 + 27
6 u = 114
1 u = 114 ÷ 6 = 19
Number of balls that Cindy had at first
= 1 u + 29 + 9 u
= 10 u + 29
= 10 x 19 + 29
= 190 + 29
= 219
(b)
Number of blue balls
= 9 u
= 9 x 19
= 171
Fraction of Cindy's balls that is blue
=
171219=
5773 Answer(s): (a) 219; (b)
5773 
