Valen, John and Bryan shared a bag of marbles. John took 27 as many marbles as Bryan. Valen took thrice as many marbles as the total John and Bryan took. After Valen had given 55 to John and 20 to Bryan, John gave 5 to Bryan. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Valen and John had at first.
| |
John |
Bryan |
Valen |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 55 |
|
- 55 |
|
| Change 2 |
|
+ 20 |
- 20 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of marbles that John and Bryan had at first
= 2 u + 7 u
= 12 u
Number of marbles that Valen had at first
= 3 x 12 u
= 27 u
The total number of marbles remains unchanged. Make the total number of marbles the same. LCM of 3 and 36 is 36.
Number of marbles that Bryan received from John and Valen
= 12 u - 7 u
= 5 u
5 u = 20 + 5
5 u = 25
1 u = 25 ÷ 5 = 5
Difference between the number marbles that Valen and John had at first
= 27 u - 2 u
= 25 u
= 25 x 5
= 125
Answer(s): 125
