Cody, Vincent and Bryan shared a bag of marbles. Vincent took 27 as many marbles as Bryan. Cody took four times as many marbles as the total Vincent and Bryan took. After Cody had given 71 to Vincent and 34 to Bryan, Vincent gave 6 to Bryan. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Cody and Vincent had at first.
| |
Vincent |
Bryan |
Cody |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 71 |
|
- 71 |
|
| Change 2 |
|
+ 34 |
- 34 |
|
| Change 3 |
- 6 |
+ 6 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of marbles that Vincent and Bryan had at first
= 2 u + 7 u
= 15 u
Number of marbles that Cody had at first
= 4 x 15 u
= 36 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 45 is 45.
Number of marbles that Bryan received from Vincent and Cody
= 15 u - 7 u
= 8 u
8 u = 34 + 6
8 u = 40
1 u = 40 ÷ 8 = 5
Difference between the number marbles that Cody and Vincent had at first
= 36 u - 2 u
= 34 u
= 34 x 5
= 170
Answer(s): 170
