Daniel, Xavier and Glen shared a bag of pens. Xavier took 25 as many pens as Glen. Daniel took twice as many pens as the total Xavier and Glen took. After Daniel had given 27 to Xavier and 8 to Glen, Xavier gave 2 to Glen. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Daniel and Xavier had at first.
| |
Xavier |
Glen |
Daniel |
Total |
| Before |
2 u |
5 u |
14 u |
21 u |
| Change 1 |
+ 27 |
|
- 27 |
|
| Change 2 |
|
+ 8 |
- 8 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x7 =
7 u |
1x7 =
7 u |
1x7 =
7 u |
3x7 =
21 u |
Total number of pens that Xavier and Glen had at first
= 2 u + 5 u
= 7 u
Number of pens that Daniel had at first
= 2 x 7 u
= 14 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 21 is 21.
Number of pens that Glen received from Xavier and Daniel
= 7 u - 5 u
= 2 u
2 u = 8 + 2
2 u = 10
1 u = 10 ÷ 2 = 5
Difference between the number pens that Daniel and Xavier had at first
= 14 u - 2 u
= 12 u
= 12 x 5
= 60
Answer(s): 60
