Liam, Owen and Vincent had the same number of balls. Vincent gave 0.6 of his balls to Owen. Then Owen gave 0.45 of his balls to Liam. Finally, after Owen gave 24 balls to Vincent, he had the same number of balls as Vincent. How many balls did Vincent have at first?
| |
Liam |
Owen |
Vincent |
| 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 Owen gave to Liam
= 0.45 x 1.6 u
= 0.72 u
The number of balls that Owen and Vincent 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 Vincent had at first
= 1 u
= 100
Answer(s): 100
