Yoko had some pink and grey balls. If she gives away 12 pink balls, the number of pink balls will be 20% of the total number of balls left. If she gives away 28 grey balls, the number of pink balls will be 25% of the total number of balls left.
- How many balls does Yoko have altogether?
- What fraction of Yoko's balls is grey?
| |
Scenario 1 |
Scenario 2 |
| |
Pink |
Grey |
Pink |
Grey |
| Before |
1 u + 12 |
4 u |
1 p |
3 p + 28 |
| Change |
- 12 |
No change |
No change |
- 28 |
| After |
1 u |
4 u |
1 p |
3 p |
(a)
20% =
20100 =
1525% =
25100 =
141 u + 12 = 1 p --- (1)
4 u = 3 p + 28
4 u - 28 = 3 p --- (2)
Make p the same.
(1)
x33 u + 36 = 3 p --- (3)
(2) = (3)
4 u - 28 = 3 u + 36
4 u - 3 u = 36 + 28
1 u = 64
Number of balls that Yoko had at first
= 1 u + 12 + 4 u
= 5 u + 12
= 5 x 64 + 12
= 320 + 12
= 332
(b)
Number of grey balls
= 4 u
= 4 x 64
= 256
Fraction of Yoko's balls that is grey
=
256332=
6483 Answer(s): (a) 332; (b)
6483 
