Elijah, Ben and Daniel shared a bag of beads. Ben took 37 as many beads as Daniel. Elijah took twice as many beads as the total Ben and Daniel took. After Elijah had given 28 to Ben and 2 to Daniel, Ben gave 7 to Daniel. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Elijah and Ben had at first.
| |
Ben |
Daniel |
Elijah |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 28 |
|
- 28 |
|
| Change 2 |
|
+ 2 |
- 2 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of beads that Ben and Daniel had at first
= 3 u + 7 u
= 10 u
Number of beads that Elijah had at first
= 2 x 10 u
= 20 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 30 is 30.
Number of beads that Daniel received from Ben and Elijah
= 10 u - 7 u
= 3 u
3 u = 2 + 7
3 u = 9
1 u = 9 ÷ 3 = 3
Difference between the number beads that Elijah and Ben had at first
= 20 u - 3 u
= 17 u
= 17 x 3
= 51
Answer(s): 51
