Vincent, Fred and Andy shared a bag of marbles. Fred took 37 as many marbles as Andy. Vincent took twice as many marbles as the total Fred and Andy took. After Vincent had given 72 to Fred and 28 to Andy, Fred gave 2 to Andy. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Vincent and Fred had at first.
| |
Fred |
Andy |
Vincent |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 72 |
|
- 72 |
|
| Change 2 |
|
+ 28 |
- 28 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of marbles that Fred and Andy had at first
= 3 u + 7 u
= 10 u
Number of marbles that Vincent had at first
= 2 x 10 u
= 20 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 30 is 30.
Number of marbles that Andy received from Fred and Vincent
= 10 u - 7 u
= 3 u
3 u = 28 + 2
3 u = 30
1 u = 30 ÷ 3 = 10
Difference between the number marbles that Vincent and Fred had at first
= 20 u - 3 u
= 17 u
= 17 x 10
= 170
Answer(s): 170
