2. In an election, there were three candidates. 3/7 of the electors voted for the winner. The runner-up received 5/8 of the remaining votes.
a. What fraction of the electors voted for the third candidate?
b. If the winner received 3021 votes more than the runner-up, how many electors voted?
To find the fraction of electors who voted for the third candidate, we need to subtract the fractions of electors who voted for the winner and the runner-up from 1 (since all the votes are accounted for).
Fraction of electors who voted for the winner: 3/7
Fraction of electors who voted for the runner-up: 5/8
Total fraction of electors who voted for the winner and runner-up: 3/7 + 5/8 = (24/56) + (35/56) = 59/56
Fraction of electors who voted for the third candidate: 1 - 59/56 = (56/56) - (59/56) = (56 - 59)/56 = -3/56
a. The fraction of electors who voted for the third candidate is -3/56.
b. Since we cannot have a negative fraction of electors, it means that there were no electors who voted for the third candidate. Therefore, we cannot determine the total number of electors who voted based on the given information.