Michael, Neave and Archie shared a bag of erasers. Neave took 27 as many erasers as Archie. Michael took four times as many erasers as the total Neave and Archie took. After Michael had given 54 to Neave and 30 to Archie, Neave gave 2 to Archie. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Michael and Neave had at first.
| |
Neave |
Archie |
Michael |
Total |
| Before |
2 u |
7 u |
36 u |
45 u |
| Change 1 |
+ 54 |
|
- 54 |
|
| Change 2 |
|
+ 30 |
- 30 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x15 =
15 u |
1x15 =
15 u |
1x15 =
15 u |
3x15 =
45 u |
Total number of erasers that Neave and Archie had at first
= 2 u + 7 u
= 15 u
Number of erasers that Michael 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 Archie received from Neave and Michael
= 15 u - 7 u
= 8 u
8 u = 30 + 2
8 u = 32
1 u = 32 ÷ 8 = 4
Difference between the number erasers that Michael and Neave had at first
= 36 u - 2 u
= 34 u
= 34 x 4
= 136
Answer(s): 136
