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