Gabriel, Bobby and Ken shared a bag of beads. Bobby took 27 as many beads as Ken. Gabriel took thrice as many beads as the total Bobby and Ken took. After Gabriel had given 99 to Bobby and 36 to Ken, Bobby gave 9 to Ken. In the end, all three of them had the same number of beads. Find the difference between the number of beads that Gabriel and Bobby had at first.
| |
Bobby |
Ken |
Gabriel |
Total |
| Before |
2 u |
7 u |
27 u |
36 u |
| Change 1 |
+ 99 |
|
- 99 |
|
| Change 2 |
|
+ 36 |
- 36 |
|
| Change 3 |
- 9 |
+ 9 |
|
|
| After |
1x12 =
12 u |
1x12 =
12 u |
1x12 =
12 u |
3x12 =
36 u |
Total number of beads that Bobby and Ken 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 Ken received from Bobby and Gabriel
= 12 u - 7 u
= 5 u
5 u = 36 + 9
5 u = 45
1 u = 45 ÷ 5 = 9
Difference between the number beads that Gabriel and Bobby had at first
= 27 u - 2 u
= 25 u
= 25 x 9
= 225
Answer(s): 225
