Mark, Billy and Fred shared a bag of beads. Billy took 27 as many beads as Fred. Mark took four times as many beads as the total Billy and Fred took. After Mark had given 132 to Billy and 78 to Fred, Billy gave 2 to Fred. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Mark and Billy had at first.
| |
Billy |
Fred |
Mark |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 132 |
|
- 132 |
|
| Change 2 |
|
+ 78 |
- 78 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of beads that Billy and Fred had at first
= 2 u + 7 u
= 15 u
Number of beads that Mark had at first
= 4 x 15 u
= 36 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 45 is 45.
Number of beads that Fred received from Billy and Mark
= 15 u - 7 u
= 8 u
8 u = 78 + 2
8 u = 80
1 u = 80 ÷ 8 = 10
Difference between the number beads that Mark and Billy had at first
= 36 u - 2 u
= 34 u
= 34 x 10
= 340
Answer(s): 340
