Archie, Gabriel and Eric shared a bag of pens. Gabriel took 27 as many pens as Eric. Archie took thrice as many pens as the total Gabriel and Eric took. After Archie had given 57 to Gabriel and 18 to Eric, Gabriel gave 7 to Eric. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Archie and Gabriel had at first.
| |
Gabriel |
Eric |
Archie |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 57 |
|
- 57 |
|
| Change 2 |
|
+ 18 |
- 18 |
|
| Change 3 |
- 7 |
+ 7 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of pens that Gabriel and Eric had at first
= 2 u + 7 u
= 12 u
Number of pens that Archie had at first
= 3 x 12 u
= 27 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 36 is 36.
Number of pens that Eric received from Gabriel and Archie
= 12 u - 7 u
= 5 u
5 u = 18 + 7
5 u = 25
1 u = 25 ÷ 5 = 5
Difference between the number pens that Archie and Gabriel had at first
= 27 u - 2 u
= 25 u
= 25 x 5
= 125
Answer(s): 125
