Ken, Vaidev and Eric shared a bag of buttons. Vaidev took 27 as many buttons as Eric. Ken took twice as many buttons as the total Vaidev and Eric took. After Ken had given 78 to Vaidev and 12 to Eric, Vaidev gave 8 to Eric. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Ken and Vaidev had at first.
| |
Vaidev |
Eric |
Ken |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 78 |
|
- 78 |
|
| Change 2 |
|
+ 12 |
- 12 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of buttons that Vaidev and Eric had at first
= 2 u + 7 u
= 9 u
Number of buttons that Ken 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 Eric received from Vaidev and Ken
= 9 u - 7 u
= 2 u
2 u = 12 + 8
2 u = 20
1 u = 20 ÷ 2 = 10
Difference between the number buttons that Ken and Vaidev had at first
= 18 u - 2 u
= 16 u
= 16 x 10
= 160
Answer(s): 160
