SOLUTION: A strange announcement was made on the radio about a local election with three candidates: Mrs Allan, Mr Baxter and Ms Campbell. �Mrs Allan beat Mr Baxter by one eighth of the tot

Question 1108214: A strange announcement was made on the radio about a local election with three candidates: Mrs Allan, Mr Baxter and Ms Campbell.
�Mrs Allan beat Mr Baxter by one eighth of the total votes cast.
Mr Baxter beat Ms Campbell by a seventh of the total votes cast.
The votes cast for Mrs Allan was 350 fewer than 3 times Ms Campbell's votes.�
How many votes did each candidate get?
I know this is a simultaneous equation problem, but I am not very good at them. I keep going round in circles and cannot figure out what the next step is.
Thank you in advance! Your help is much appreciated!
Found 2 solutions by Boreal, Alan3354:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Total votes cast=x
A-B=(1/8)x
B-C=(1/7)x
A=3C-350
A+B+C=x
A=B +(1/8)x from the first
B+(1/8)x+B+C=x
2B+C=(7/8)x
B-C=(1/7)x from the second
3B=(57/56)x using common denominator of 56
B=(19/56)x
Then C=(11/56)x substituting into B-C=(1/7)x
A=(26/56)x
Those three =x
A=3C-350, so (26/56)x=(33/56)x-350, and -(7/56)x=-350=(-1/8)x, so that x=2800 votes
A got 26/56 of them or 1300
B got 19/56 of them or 950
C got 11/56 of them or 550
ANSWER

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!

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