Sean, Howard and Ian had the same number of balls. Ian gave 0.6 of his balls to Howard. Then Howard gave 0.45 of his balls to Sean. Finally, after Howard gave 24 balls to Ian, he had the same number of balls as Ian. How many balls did Ian have at first?
| |
Sean |
Howard |
Ian |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.6 u |
- 0.6 u |
| After 1 |
1 u |
1.6 u |
0.4 u |
| Change 2 |
+ 0.72 u |
- 0.72 u |
|
| After 2 |
1.72 u |
0.88 u |
0.4 u |
| Change 3 |
|
- 24 |
+ 24 |
| After 3 |
1.72 u |
0.88 u - 24 |
0.4 u + 24 |
Number of balls that Howard gave to Sean
= 0.45 x 1.6 u
= 0.72 u
The number of balls that Howard and Ian had in the end is the same.
0.88 u - 24 = 0.4 u + 24
0.88 u - 0.4 u = 24 + 24
0.48 u = 48
1 u = 48 ÷ 0.48 = 100
Number of balls that Ian had at first
= 1 u
= 100
Answer(s): 100
