The day after the school election it was reported that Danny won the election for class president. For every three votes his opponent received, Danny received 5 votes. Every student voted exactly once. If the students voted only for either Danny or his opponent and Danny's opponent received 312 votes, how many students voted in the election?
The day after the school election it was reported that Danny won the election for class president. For every three votes his opponent received, Danny received 5 votes. Every student voted exactly once. If the students voted only for either Danny or his opponent and Danny's opponent received 312 votes, how many students voted in the election?
Danny received = 5 of every 8 votes
Opponent received = 3 of every 8 votes
Let V stand for the total number of votes cast.
The opponent's 3/8 of the votes was 312 so (3/8) times V = 312
(3/8)(V) = 312
V = (312)/(3/8) ( i.e., 312 divided by 3/8 )
To divide by a fraction, you invert the divisor and multiply
V = (312) x (8/3) = 2496/8 = 832 total votes
.
