Reggie, Henry and Archie shared a bag of buttons. Henry took 27 as many buttons as Archie. Reggie took four times as many buttons as the total Henry and Archie took. After Reggie had given 88 to Henry and 38 to Archie, Henry gave 10 to Archie. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Reggie and Henry had at first.
| |
Henry |
Archie |
Reggie |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 88 |
|
- 88 |
|
| Change 2 |
|
+ 38 |
- 38 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of buttons that Henry and Archie had at first
= 2 u + 7 u
= 15 u
Number of buttons that Reggie had at first
= 4 x 15 u
= 36 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 45 is 45.
Number of buttons that Archie received from Henry and Reggie
= 15 u - 7 u
= 8 u
8 u = 38 + 10
8 u = 48
1 u = 48 ÷ 8 = 6
Difference between the number buttons that Reggie and Henry had at first
= 36 u - 2 u
= 34 u
= 34 x 6
= 204
Answer(s): 204
