SOLUTION: vivienne, john, and nassim ran for 6th grade class president. overall, 84 6th grade scholars voted in the class president election vivienne got 2 votes for every vote john g

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: vivienne, john, and nassim ran for 6th grade class president. overall, 84 6th grade scholars voted in the class president election vivienne got 2 votes for every vote john g      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1010028: vivienne, john, and nassim ran for 6th grade class president. overall, 84 6th grade scholars voted in the class president election

vivienne got 2 votes for every vote john got.
nassim got 2 votes for every vote vivienne got.
how many votes did vivienne got?
I really didn't understand how to answer the question but heres what I got.
John x 1 got 5 votes
Vivienne x 2 got 10 votes
Nassim x 4 got 40 votes
Answer 55 votes in total
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This problem makes an assumption. There were
3 people running for office and 84 people voted.
Did all the voters vote for one of the three?
Did any abstain from voting?
So, they all must have voted for one of the three
----------------------------------------
(1) +v+%2B+j+%2B+n+=+84+
(2) +v+=+2j+
(3) +n+=+2v+
--------------------
There are 3 equations and 3 unknowns,
so it's solvable
--------------
(2) +j+=+v%2F2+
Substitute (2) and (3) into (1)
(1) +v+%2B+j+%2B+n+=+84+
(1) +v+%2B+v%2F2+%2B+2v+=+84+
(1) +2v+%2B+v+%2B+4v+=+168
(1) +7v+=+168+
(1) +v+=+24+
and
(2) +j+=+v%2F2+
(2) +j+=+24%2F2+
(2) +j+=+12+
and
(3) +n+=+2v+
(3) +n+=+2%2A24+
(3) +n+=+48+
------------------
John got 12 votes
Vivienne got 24 votes
Nassim got 48 votes
-------------------
check:
(1) +v+%2B+j+%2B+n+=+84+
(1) +24+%2B12+%2B+48+=+84+
(1) +84+=+84+
OK