Luis, Luke and Sean shared a bag of marbles. Luke took 37 as many marbles as Sean. Luis took twice as many marbles as the total Luke and Sean took. After Luis had given 79 to Luke and 21 to Sean, Luke gave 9 to Sean. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Luis and Luke had at first.
| |
Luke |
Sean |
Luis |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 79 |
|
- 79 |
|
| Change 2 |
|
+ 21 |
- 21 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of marbles that Luke and Sean had at first
= 3 u + 7 u
= 10 u
Number of marbles that Luis 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 Sean received from Luke and Luis
= 10 u - 7 u
= 3 u
3 u = 21 + 9
3 u = 30
1 u = 30 ÷ 3 = 10
Difference between the number marbles that Luis and Luke had at first
= 20 u - 3 u
= 17 u
= 17 x 10
= 170
Answer(s): 170
