Caden, Asher and Howard shared a bag of beads. Asher took 35 as many beads as Howard. Caden took twice as many beads as the total Asher and Howard took. After Caden had given 28 to Asher and 4 to Howard, Asher gave 8 to Howard. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Caden and Asher had at first.
| |
Asher |
Howard |
Caden |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 28 |
|
- 28 |
|
| Change 2 |
|
+ 4 |
- 4 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of beads that Asher and Howard had at first
= 3 u + 5 u
= 8 u
Number of beads that Caden had at first
= 2 x 8 u
= 16 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 24 is 24.
Number of beads that Howard received from Asher and Caden
= 8 u - 5 u
= 3 u
3 u = 4 + 8
3 u = 12
1 u = 12 ÷ 3 = 4
Difference between the number beads that Caden and Asher had at first
= 16 u - 3 u
= 13 u
= 13 x 4
= 52
Answer(s): 52
