Rachel had some grey and blue balls. If she gives away 27 grey balls, the number of grey balls will be 20% of the total number of balls left. If she gives away 12 blue balls, the number of grey balls will be 25% of the total number of balls left.
- How many balls does Rachel have altogether?
- What fraction of Rachel's balls is blue?
| |
Scenario 1 |
Scenario 2 |
| |
Grey |
Blue |
Grey |
Blue |
| Before |
1 u + 27 |
4 u |
1 p |
3 p + 12 |
| Change |
- 27 |
No change |
No change |
- 12 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 27 = 1 p --- (1)
4 u = 3 p + 12
4 u - 12 = 3 p --- (2)
Make p the same.
(1)
x33 u + 81 = 3 p --- (3)
(2) = (3)
4 u - 12 = 3 u + 81
4 u - 3 u = 81 + 12
1 u = 93
Number of balls that Rachel had at first
= 1 u + 27 + 4 u
= 5 u + 27
= 5 x 93 + 27
= 465 + 27
= 492
(b)
Number of blue balls
= 4 u
= 4 x 93
= 372
Fraction of Rachel's balls that is blue
=
372492=
3141 Answer(s): (a) 492; (b)
3141 
