Zane, Luis and Fred shared a bag of pens. Luis took 37 as many pens as Fred. Zane took twice as many pens as the total Luis and Fred took. After Zane had given 80 to Luis and 20 to Fred, Luis gave 10 to Fred. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Zane and Luis had at first.
| |
Luis |
Fred |
Zane |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 80 |
|
- 80 |
|
| Change 2 |
|
+ 20 |
- 20 |
|
| Change 3 |
- 10 |
+ 10 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of pens that Luis and Fred had at first
= 3 u + 7 u
= 10 u
Number of pens that Zane had at first
= 2 x 10 u
= 20 u
The total number of pens remains unchanged. Make the total number of pens the same. LCM of 3 and 30 is 30.
Number of pens that Fred received from Luis and Zane
= 10 u - 7 u
= 3 u
3 u = 20 + 10
3 u = 30
1 u = 30 ÷ 3 = 10
Difference between the number pens that Zane and Luis had at first
= 20 u - 3 u
= 17 u
= 17 x 10
= 170
Answer(s): 170
