Exercise 30 Page 730

We are given a table showing the results of an election for mayor.

Votes by Precinct
	Precinct
Candidate	1	2	3	4
Greene	373	285	479	415
Jackson	941	871	114	97
Voigt	146	183	728	682

The town will hold a runoff election between the top two candidates if no one received more than 50 percent of the votes. We want to know if the town should hold this runoff. To find out, we will start by using matrices to organize the data. [ c 373 941 146 ] [ c 285 871 183 ] [ c 479 114 728 ] [ c 415 97 682 ] We have 3* 1 matrices: there are 3 candidates per 1 precinct represented by the data. The matrices are the same size, so we can add them. Let's do it!

373 941 146 + 285 871 183 + 479 114 728 + 415 97 682

Add matrices

373 +285 +479+415 941 +871+114+97 146+183+1728+682

AddTerms

Add terms

1552 2023 1739

These are the total votes obtained by each candidate. We want to know the percent of votes, so we need to find the total votes of all election. To do so, we will sum all the entries in the column of the matrix. 1552 +2023 +1739 = 5314 Now that we have the total votes, we will divide the matrix by 5314 and then multiply by 100.

1552 2023 1739

Div

Divide by 5314

0.28 0.38 0.33

Multiply matrix by ( 100)

0.28 ( 100) 0.38 ( 100) 0.33( 100)

Multiply

Multiply

28 38 33

We can see that no one received more than the 50 percent of votes. We can also see that the last two rows of the matrix shows the greatest numbers. Therefore, the town should hold a runoff for Jackson and Voigt.