Question

The losing candidate in a mayoral election received 10,200 votes, which represented 30% of all votes cast in the election.

A. Dorian claims that the total number of votes cast in the mayoral election was 3,060. Dorian made a mistake in his calculations. Why is his claim not reasonable? Explain your answer.

B. Find the total number of votes cast in the mayoral election. Explain how you found your answer.

Answer 1

well, in the election, the losing candidate received 10200 votes, and we know that's 30% of the whole votes cast, le's say the whole amount is "x" or namely 100%.

B)

`\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 10200&30\\ x&100 \end{array}\implies \cfrac{10200}{x}=\cfrac{30}{100}\implies \cfrac{10200}{x}=\cfrac{3}{10} \\\\\\ 102000=3x\implies \cfrac{102000}{3}=x\implies 34000=x`

A)

Dorian's 3060 is really 30% of 10200, however, the losing candidate received 30% of the total votes cast, and that is 10200, so Dorian mistakenly is using 30% of the 30% received by the losing candidate as point of reference for her total.