Reggie, Ethan and Sean shared a bag of buttons. Ethan took 27 as many buttons as Sean. Reggie took twice as many buttons as the total Ethan and Sean took. After Reggie had given 57 to Ethan and 6 to Sean, Ethan gave 8 to Sean. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Reggie and Ethan had at first.
| |
Ethan |
Sean |
Reggie |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 57 |
|
- 57 |
|
| Change 2 |
|
+ 6 |
- 6 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of buttons that Ethan and Sean had at first
= 2 u + 7 u
= 9 u
Number of buttons that Reggie had at first
= 2 x 9 u
= 18 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 27 is 27.
Number of buttons that Sean received from Ethan and Reggie
= 9 u - 7 u
= 2 u
2 u = 6 + 8
2 u = 14
1 u = 14 ÷ 2 = 7
Difference between the number buttons that Reggie and Ethan had at first
= 18 u - 2 u
= 16 u
= 16 x 7
= 112
Answer(s): 112
