Fabian, Carl and Cody shared a bag of marbles. Carl took 27 as many marbles as Cody. Fabian took four times as many marbles as the total Carl and Cody took. After Fabian had given 109 to Carl and 59 to Cody, Carl gave 5 to Cody. In the end, all three of them had the same number of marbles. Find the difference between the number of marbles that Fabian and Carl had at first.
| |
Carl |
Cody |
Fabian |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 109 |
|
- 109 |
|
| Change 2 |
|
+ 59 |
- 59 |
|
| Change 3 |
- 5 |
+ 5 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of marbles that Carl and Cody had at first
= 2 u + 7 u
= 15 u
Number of marbles that Fabian 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 Cody received from Carl and Fabian
= 15 u - 7 u
= 8 u
8 u = 59 + 5
8 u = 64
1 u = 64 ÷ 8 = 8
Difference between the number marbles that Fabian and Carl had at first
= 36 u - 2 u
= 34 u
= 34 x 8
= 272
Answer(s): 272
