SOLUTION: Kim was selected class president. She received 3 votes for every 2 that Amy got. No one else ran. However, if 8 of the people who voted for Kim had voted for Amy instead, Kim wo

Algebra ->  Algebra  -> Proportions  -> Lessons  -> Proportions -> SOLUTION: Kim was selected class president. She received 3 votes for every 2 that Amy got. No one else ran. However, if 8 of the people who voted for Kim had voted for Amy instead, Kim wo      Log On

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Question 172838: Kim was selected class president. She received 3 votes for every 2 that Amy got. No one else ran. However, if 8 of the people who voted for Kim had voted for Amy instead, Kim would have received only 1 vote for every 2 that Amy would have gotten. How many people voted?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
ok the easiest way to set this up is with proportions
:
lets call votes kim receives k and votes amy receives a
:
k%2Fa=3%2F2--->2k=3a---->k=3a/2......eq 1
:
%28k-8%29%2F%28a%2B8%29=1%2F2----->a+8=2(k-8)--->a+8=2k-16--->a-2k=-24....eq 2
:
lets substitute k's value in eq 1 into eq 2
:
a-2(3a/2)=-24
:
a-3a--24
:
-2a=-24
:
highlight%28a=12%29votes for amy
:
highlight%28k=3%2812%29%2F2=18%29votes for kim
Total of people who votedhighlight%2818%2B12=30%29