Ryan, Glen and Ivan had the same number of marbles. Ivan gave 0.5 of his marbles to Glen. Then Glen gave 0.25 of his marbles to Ryan. Finally, after Glen gave 20 marbles to Ivan, he had the same number of marbles as Ivan. How many marbles did Ivan have at first?
| |
Ryan |
Glen |
Ivan |
| Before |
1 u |
1 u |
1 u |
| Change 1 |
|
+ 0.5 u |
- 0.5 u |
| After 1 |
1 u |
1.5 u |
0.5 u |
| Change 2 |
+ 0.375 u |
- 0.375 u |
|
| After 2 |
1.375 u |
1.125 u |
0.5 u |
| Change 3 |
|
- 20 |
+ 20 |
| After 3 |
1.375 u |
1.125 u - 20 |
0.5 u + 20 |
Number of marbles that Glen gave to Ryan
= 0.25 x 1.5 u
= 0.375 u
The number of marbles that Glen and Ivan had in the end is the same.
1.125 u - 20 = 0.5 u + 20
1.125 u - 0.5 u = 20 + 20
0.625 u = 40
1 u = 40 ÷ 0.625 = 64
Number of marbles that Ivan had at first
= 1 u
= 64
Answer(s): 64
