Question

A newspaper reported that candidate Williams received 13,500 more votes that her opponebt Ms. Smith, and that 42,310 votes were cast in the election. How many votes were cast for each candidate?

Answer 1

Williams received 27,905 votes in the election.

Ms. Smith received 14,405 votes in the election.

Explanation:

Let x be the number of votes cast to Ms. Smith.

We have been given that candidate Williams received 13,500 more votes that her opponent Ms. Smith. So number of votes in favor of Williams would be
`x+13,500`.

We are also told that 42,310 votes were cast in the election. This means that number of votes in favor of Williams and Ms. Smith is equal to 42,310. We can represent this information in an equation as:

`x+x+13,500=42,310`

`2x+13,500=42,310`

`2x+13,500-13,500=42,310-13,500`

`2x=28,810`

`(2x)/(2)=(28,810)/(2)`

`x=14,405`

Therefore, Ms. Smith received 14,405 votes in the election.

To find number of votes cast to Williams, we will add 13,500 to 14,405 as:

`x+13,500\rightarrow 14,405+13,500=27,905`

Therefore, Williams received 27,905 votes in the election.