In a mayoral election, the number of votes for the incumbent was 25% more than the number for the opponent. Altogether, the two candidates received 5,175 votes. How many votes did the incumbent mayor receive?
Answer (3)
100\%+25\%=125\%=\frac{125}{100}=1.25\\\\x;y-number\ of\ votes\ cast\ for\ candidates\ for\ mayor\\\\ \left\{\begin{array}{ccc}x=1.25y\\x+y=5175\end{array}\right\\\\subtitute:\\\\1.25y+y=5175\\2.25y=5175\ \ \ \ |divide\ both\ sides\ by\ 2.25\\\boxed{y=2300}\\\\x=1.25\times2300=2875\\\\Answer:\boxed{\boxed{2875}}
In the mayoral election where the incumbent received 25% more votes than their opponent, with a total of 5175 votes, the incumbent mayor received 2875 votes.
The question is about determining how many votes the incumbent mayor received in a mayoral election where they got 25% more votes than their opponent, with a total of 5175 votes for both candidates.
To solve this, let's denote the number of votes for the opponent as V. The incumbent received 25% more than this, which can be expressed as V + 0.25V or 1.25V. Together, they received 5175 votes, which can be represented as:
V + 1.25V = 5175
Combining like terms gives us:
2.25V = 5175
V = 2300 (votes for the opponent)
Now, to find the incumbent's votes, we multiply the opponent's votes by 1.25:
Incumbent votes = 2300 * 1.25
Incumbent votes = 2875
Therefore, the incumbent mayor received 2875 votes.
The incumbent mayor received 2,875 votes. This was calculated by setting up equations based on the information provided about the total votes and the relationship between the votes for the incumbent and the opponent. By solving these equations, we determined the number of votes each candidate received.
;
