Vincent, Howard and Eric shared a bag of buttons. Howard took 35 as many buttons as Eric. Vincent took twice as many buttons as the total Howard and Eric took. After Vincent had given 38 to Howard and 18 to Eric, Howard gave 3 to Eric. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Vincent and Howard had at first.
| |
Howard |
Eric |
Vincent |
Total |
| Before |
3 u |
5 u |
16 u |
24 u |
| Change 1 |
+ 38 |
|
- 38 |
|
| Change 2 |
|
+ 18 |
- 18 |
|
| Change 3 |
- 3 |
+ 3 |
|
|
| After |
1x8 =
8 u |
1x8 =
8 u |
1x8 =
8 u |
3x8 =
24 u |
Total number of buttons that Howard and Eric had at first
= 3 u + 5 u
= 8 u
Number of buttons that Vincent had at first
= 2 x 8 u
= 16 u
The total number of buttons remains unchanged. Make the total number of buttons the same. LCM of 3 and 24 is 24.
Number of buttons that Eric received from Howard and Vincent
= 8 u - 5 u
= 3 u
3 u = 18 + 3
3 u = 21
1 u = 21 ÷ 3 = 7
Difference between the number buttons that Vincent and Howard had at first
= 16 u - 3 u
= 13 u
= 13 x 7
= 91
Answer(s): 91
