Billy, Elijah and Asher shared a bag of erasers. Elijah took 27 as many erasers as Asher. Billy took thrice as many erasers as the total Elijah and Asher took. After Billy had given 99 to Elijah and 36 to Asher, Elijah gave 9 to Asher. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Billy and Elijah had at first.
| |
Elijah |
Asher |
Billy |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 99 |
|
- 99 |
|
| Change 2 |
|
+ 36 |
- 36 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of erasers that Elijah and Asher had at first
= 2 u + 7 u
= 12 u
Number of erasers that Billy had at first
= 3 x 12 u
= 27 u
The total number of erasers remains unchanged. Make the total number of erasers the same. LCM of 3 and 36 is 36.
Number of erasers that Asher received from Elijah and Billy
= 12 u - 7 u
= 5 u
5 u = 36 + 9
5 u = 45
1 u = 45 ÷ 5 = 9
Difference between the number erasers that Billy and Elijah had at first
= 27 u - 2 u
= 25 u
= 25 x 9
= 225
Answer(s): 225
