Fabian, Ian and Ben shared a bag of erasers. Ian took 27 as many erasers as Ben. Fabian took twice as many erasers as the total Ian and Ben took. After Fabian had given 74 to Ian and 16 to Ben, Ian gave 4 to Ben. In the end, all three of them had the same number of erasers. Find the difference between the number of erasers that Fabian and Ian had at first.
| |
Ian |
Ben |
Fabian |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 74 |
|
- 74 |
|
| Change 2 |
|
+ 16 |
- 16 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of erasers that Ian and Ben had at first
= 2 u + 7 u
= 9 u
Number of erasers that Fabian had at first
= 2 x 9 u
= 18 u
The total number of erasers remains unchanged. Make the total number of erasers the same. LCM of 3 and 27 is 27.
Number of erasers that Ben received from Ian and Fabian
= 9 u - 7 u
= 2 u
2 u = 16 + 4
2 u = 20
1 u = 20 ÷ 2 = 10
Difference between the number erasers that Fabian and Ian had at first
= 18 u - 2 u
= 16 u
= 16 x 10
= 160
Answer(s): 160
