Archie, Fabian and Vaidev shared a bag of buttons. Fabian took 27 as many buttons as Vaidev. Archie took thrice as many buttons as the total Fabian and Vaidev took. After Archie had given 77 to Fabian and 28 to Vaidev, Fabian gave 7 to Vaidev. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Archie and Fabian had at first.
| |
Fabian |
Vaidev |
Archie |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 77 |
|
- 77 |
|
| Change 2 |
|
+ 28 |
- 28 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of buttons that Fabian and Vaidev had at first
= 2 u + 7 u
= 12 u
Number of buttons that Archie 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 Vaidev received from Fabian and Archie
= 12 u - 7 u
= 5 u
5 u = 28 + 7
5 u = 35
1 u = 35 ÷ 5 = 7
Difference between the number buttons that Archie and Fabian had at first
= 27 u - 2 u
= 25 u
= 25 x 7
= 175
Answer(s): 175
