Carl, Fred and Simon shared a bag of marbles. Fred took 27 as many marbles as Simon. Carl took thrice as many marbles as the total Fred and Simon took. After Carl had given 42 to Fred and 18 to Simon, Fred gave 2 to Simon. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Carl and Fred had at first.
| |
Fred |
Simon |
Carl |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 42 |
|
- 42 |
|
| Change 2 |
|
+ 18 |
- 18 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of marbles that Fred and Simon had at first
= 2 u + 7 u
= 12 u
Number of marbles that Carl 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 Simon received from Fred and Carl
= 12 u - 7 u
= 5 u
5 u = 18 + 2
5 u = 20
1 u = 20 ÷ 5 = 4
Difference between the number marbles that Carl and Fred had at first
= 27 u - 2 u
= 25 u
= 25 x 4
= 100
Answer(s): 100
