SOLUTION: In an election A got 400 more votes than B. If 1/8 of the votes for A had gone to B, B would have had 500 more votes than A. In the original election how many votes did A and B get

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: In an election A got 400 more votes than B. If 1/8 of the votes for A had gone to B, B would have had 500 more votes than A. In the original election how many votes did A and B get      Log On


   

Question 249982: In an election A got 400 more votes than B. If 1/8 of the votes for A had gone to B, B would have had 500 more votes than A. In the original election how many votes did A and B get?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a=b+400
a+b=x
a-1a/8+500=b+a/8
substitute a+b for x
a-a/8+500=b+a/8
substitute b+400 for a
b+400-(b+400)/(8)+500=b+(b+400)/8
factor
(1/8)*(-b-400)+b+900=b+(1/8)*(b+400)
expand out terms
b7/8+850=9b/8+50
get b on one side
and numbers on other
800=2b/8
800=b/4
3200=b
a=3200+400=3600
a+b=6800
3600/8=450
check
if 450 votes for a became 450 for b
then
3650 for b
3150 would be for a
500 more for b
ok