Peter, Carl and Ahmad shared a bag of pens. Carl took 27 as many pens as Ahmad. Peter took twice as many pens as the total Carl and Ahmad took. After Peter had given 80 to Carl and 10 to Ahmad, Carl gave 10 to Ahmad. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Peter and Carl had at first.
| |
Carl |
Ahmad |
Peter |
Total |
| Before |
2 u |
7 u |
18 u |
27 u |
| Change 1 |
+ 80 |
|
- 80 |
|
| Change 2 |
|
+ 10 |
- 10 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x9 =
9 u |
1x9 =
9 u |
1x9 =
9 u |
3x9 =
27 u |
Total number of pens that Carl and Ahmad had at first
= 2 u + 7 u
= 9 u
Number of pens that Peter 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 Ahmad received from Carl and Peter
= 9 u - 7 u
= 2 u
2 u = 10 + 10
2 u = 20
1 u = 20 ÷ 2 = 10
Difference between the number pens that Peter and Carl had at first
= 18 u - 2 u
= 16 u
= 16 x 10
= 160
Answer(s): 160
