Tommy, Jack and Howard shared a bag of buttons. Jack took 27 as many buttons as Howard. Tommy took thrice as many buttons as the total Jack and Howard took. After Tommy had given 50 to Jack and 10 to Howard, Jack gave 10 to Howard. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Tommy and Jack had at first.
| |
Jack |
Howard |
Tommy |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 50 |
|
- 50 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of buttons that Jack and Howard had at first
= 2 u + 7 u
= 12 u
Number of buttons that Tommy 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 Howard received from Jack and Tommy
= 12 u - 7 u
= 5 u
5 u = 10 + 10
5 u = 20
1 u = 20 ÷ 5 = 4
Difference between the number buttons that Tommy and Jack had at first
= 27 u - 2 u
= 25 u
= 25 x 4
= 100
Answer(s): 100
