Gabriel, Ken and Will shared a bag of pens. Ken took 27 as many pens as Will. Gabriel took twice as many pens as the total Ken and Will took. After Gabriel had given 53 to Ken and 10 to Will, Ken gave 4 to Will. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Gabriel and Ken had at first.
| |
Ken |
Will |
Gabriel |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 53 |
|
- 53 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 4 |
+ 4 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of pens that Ken and Will had at first
= 2 u + 7 u
= 9 u
Number of pens that Gabriel had at first
= 2 x 9 u
= 18 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 27 is 27.
Number of pens that Will received from Ken and Gabriel
= 9 u - 7 u
= 2 u
2 u = 10 + 4
2 u = 14
1 u = 14 ÷ 2 = 7
Difference between the number pens that Gabriel and Ken had at first
= 18 u - 2 u
= 16 u
= 16 x 7
= 112
Answer(s): 112
