Gabriel, Fabian and Justin shared a bag of beads. Fabian took 27 as many beads as Justin. Gabriel took thrice as many beads as the total Fabian and Justin took. After Gabriel had given 92 to Fabian and 43 to Justin, Fabian gave 2 to Justin. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Gabriel and Fabian had at first.
| |
Fabian |
Justin |
Gabriel |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 92 |
|
- 92 |
|
| Change 2 |
|
+ 43 |
- 43 |
|
| Change 3 |
- 2 |
+ 2 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of beads that Fabian and Justin had at first
= 2 u + 7 u
= 12 u
Number of beads that Gabriel had at first
= 3 x 12 u
= 27 u
The total number of beads remains unchanged. Make the total number of beads the same. LCM of 3 and 36 is 36.
Number of beads that Justin received from Fabian and Gabriel
= 12 u - 7 u
= 5 u
5 u = 43 + 2
5 u = 45
1 u = 45 ÷ 5 = 9
Difference between the number beads that Gabriel and Fabian had at first
= 27 u - 2 u
= 25 u
= 25 x 9
= 225
Answer(s): 225
