Dylan, Reggie and Fabian shared a bag of marbles. Reggie took 37 as many marbles as Fabian. Dylan took twice as many marbles as the total Reggie and Fabian took. After Dylan had given 45 to Reggie and 15 to Fabian, Reggie gave 3 to Fabian. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Dylan and Reggie had at first.
| |
Reggie |
Fabian |
Dylan |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 45 |
|
- 45 |
|
| Change 2 |
|
+ 15 |
- 15 |
|
| Change 3 |
- 3 |
+ 3 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of marbles that Reggie and Fabian had at first
= 3 u + 7 u
= 10 u
Number of marbles that Dylan 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 Fabian received from Reggie and Dylan
= 10 u - 7 u
= 3 u
3 u = 15 + 3
3 u = 18
1 u = 18 ÷ 3 = 6
Difference between the number marbles that Dylan and Reggie had at first
= 20 u - 3 u
= 17 u
= 17 x 6
= 102
Answer(s): 102
