Ethan, Harry and Bobby shared a bag of buttons. Harry took 27 as many buttons as Bobby. Ethan took thrice as many buttons as the total Harry and Bobby took. After Ethan had given 47 to Harry and 13 to Bobby, Harry gave 7 to Bobby. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Ethan and Harry had at first.
| |
Harry |
Bobby |
Ethan |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 47 |
|
- 47 |
|
| Change 2 |
|
+ 13 |
- 13 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of buttons that Harry and Bobby had at first
= 2 u + 7 u
= 12 u
Number of buttons that Ethan had at first
= 3 x 12 u
= 27 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 36 is 36.
Number of buttons that Bobby received from Harry and Ethan
= 12 u - 7 u
= 5 u
5 u = 13 + 7
5 u = 20
1 u = 20 ÷ 5 = 4
Difference between the number buttons that Ethan and Harry had at first
= 27 u - 2 u
= 25 u
= 25 x 4
= 100
Answer(s): 100
