Warren, John and Ryan shared a bag of marbles. John took 27 as many marbles as Ryan. Warren took four times as many marbles as the total John and Ryan took. After Warren had given 93 to John and 54 to Ryan, John gave 2 to Ryan. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Warren and John had at first.
| |
John |
Ryan |
Warren |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 93 |
|
- 93 |
|
| Change 2 |
|
+ 54 |
- 54 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of marbles that John and Ryan had at first
= 2 u + 7 u
= 15 u
Number of marbles that Warren 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 Ryan received from John and Warren
= 15 u - 7 u
= 8 u
8 u = 54 + 2
8 u = 56
1 u = 56 ÷ 8 = 7
Difference between the number marbles that Warren and John had at first
= 36 u - 2 u
= 34 u
= 34 x 7
= 238
Answer(s): 238
