Tim, Gabriel and Tommy shared a bag of pens. Gabriel took 37 as many pens as Tommy. Tim took twice as many pens as the total Gabriel and Tommy took. After Tim had given 43 to Gabriel and 7 to Tommy, Gabriel gave 8 to Tommy. In the end, all three of them had the same number of pens. Find the difference between the number of pens that Tim and Gabriel had at first.
| |
Gabriel |
Tommy |
Tim |
Total |
| Before |
3 u |
7 u |
20 u |
30 u |
| Change 1 |
+ 43 |
|
- 43 |
|
| Change 2 |
|
+ 7 |
- 7 |
|
| Change 3 |
- 8 |
+ 8 |
|
|
| After |
1x10 =
10 u |
1x10 =
10 u |
1x10 =
10 u |
3x10 =
30 u |
Total number of pens that Gabriel and Tommy had at first
= 3 u + 7 u
= 10 u
Number of pens that Tim 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 Tommy received from Gabriel and Tim
= 10 u - 7 u
= 3 u
3 u = 7 + 8
3 u = 15
1 u = 15 ÷ 3 = 5
Difference between the number pens that Tim and Gabriel had at first
= 20 u - 3 u
= 17 u
= 17 x 5
= 85
Answer(s): 85
