Oscar, Henry and Tim shared a bag of buttons. Henry took 27 as many buttons as Tim. Oscar took twice as many buttons as the total Henry and Tim took. After Oscar had given 31 to Henry and 5 to Tim, Henry gave 3 to Tim. In the end, all three of them had the same number of buttons. Find the difference between the number of buttons that Oscar and Henry had at first.
| |
Henry |
Tim |
Oscar |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 31 |
|
- 31 |
|
| Change 2 |
|
+ 5 |
- 5 |
|
| Change 3 |
- 3 |
+ 3 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of buttons that Henry and Tim had at first
= 2 u + 7 u
= 9 u
Number of buttons that Oscar 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 Tim received from Henry and Oscar
= 9 u - 7 u
= 2 u
2 u = 5 + 3
2 u = 8
1 u = 8 ÷ 2 = 4
Difference between the number buttons that Oscar and Henry had at first
= 18 u - 2 u
= 16 u
= 16 x 4
= 64
Answer(s): 64
