In an election there were 3 candidates 3/7 of the electors voted for the winner. The runner up received 5/8 of the remaining votes, what fraction of the electors voted for the third candidate
The final answer will be 3/14
3/14
Let the elecctors b x
3/7*x=3x/7
Remainder=x-3x/74x/7
Runner up receives 5/8 of the remaining...5/8*4x/7=5x/14
Remainder=x-5x/14=9x/14
Fraction of third candidate will b
9x/14-3x/73x/14
Ansa is 3/14 while x is the electors voted
Where did they get the 4x dat warar added to 5x\14 to make 9x\14
To find the fraction of electors who voted for the third candidate, we need to first determine the fraction of electors who voted for the winner and the runner-up, and then subtract that total from 1 (since the remaining fraction would be the portion voting for the third candidate).
Let's calculate step by step:
Step 1: Finding the fraction of electors who voted for the winner.
The problem states that 3/7 of the electors voted for the winner. Therefore, the fraction can be written as 3/7.
Step 2: Finding the fraction of electors who voted for the runner-up.
The problem says that the runner-up received 5/8 of the remaining votes. Since the votes for the winner already accounted for 3/7 of the electors, we need to subtract that fraction from 1 and then multiply by the remaining fraction (5/8) to find the votes for the runner-up.
Remaining fraction = 1 - 3/7 = 4/7
Votes for the runner-up = (4/7) * (5/8) = 20/56 simplifying to 5/14
Step 3: Finding the fraction of electors who voted for the third candidate.
Now, we need to find the remaining fraction of electors who voted for the third candidate. Since the fractions for the winner and the runner-up already accounted for a portion of the electors, we subtract both fractions from 1.
Remaining fraction for the third candidate = 1 - (3/7) - (5/14)
To simplify, let's get a common denominator:
Remaining fraction for the third candidate = 14/14 - 6/14 - 5/14
Remaining fraction for the third candidate = (14 - 6 - 5)/14
Remaining fraction for the third candidate = 3/14
Therefore, 3/14 of the electors voted for the third candidate.