Andy, Owen and Howard shared a bag of erasers. Owen took 27 as many erasers as Howard. Andy took four times as many erasers as the total Owen and Howard took. After Andy had given 48 to Owen and 15 to Howard, Owen gave 9 to Howard. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Andy and Owen had at first.
| |
Owen |
Howard |
Andy |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 48 |
|
- 48 |
|
| Change 2 |
|
+ 15 |
- 15 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of erasers that Owen and Howard had at first
= 2 u + 7 u
= 15 u
Number of erasers that Andy had at first
= 4 x 15 u
= 36 u
The total number of erasers remains unchanged. Make the total number of erasers the same. LCM of 3 and 45 is 45.
Number of erasers that Howard received from Owen and Andy
= 15 u - 7 u
= 8 u
8 u = 15 + 9
8 u = 24
1 u = 24 ÷ 8 = 3
Difference between the number erasers that Andy and Owen had at first
= 36 u - 2 u
= 34 u
= 34 x 3
= 102
Answer(s): 102
