Linear Equation Word Problems

Question

In an election between two candidates, 510 votes were cast. If the winner received 380 more votes than the loser, how many votes did the winner receive?

Answer 1

As a linear system, let x represent one candidate and y represent the other candidate. We know there was a total vote count of 510.

 

The first linear equation becomes: x + y = 510, because the votes for x and the votes for y total 510.

 

We also know one candidate received 380 more votes that the other candidate.

 

The second linear equation becomes: x - y = 380, because the difference in votes for one candidate is 380.

 

Next, solve the two linear equations:

 

                    x + y = 510

                    x -  y = 380

                   --------------

 

Adding the two equations together eliminates the y variable giving:

 

                      2x = 890

 

Divide both sides by 2 giving:  x = 445.

 

So one candidate received 445 votes. To find out how many votes the other candidate received, substitute for x in either of the two original equations:

 

                     445 + y = 510

 

Subtract 445 from both sides giving: y = 510 - 445

 

Or y = 65.

 

Therefore, one candidate received 445 votes and the other candidate received 65 votes.

 

Questions?

Answer 2

Hi Chris,

 

Let's translate the English into math. . . .

 

If the loser received X votes, then the winner received X + 380 votes.

 

The total votes equaled 510 so X + X + 380 = 510

 

Now combine like terms --> 2X + 380 = 510

 

Subtract 380 from both sides --> 2X = 130

 

Divide both sides by 2 --> X = 65

 

And the winner received 380 more votes --> 380 + 65 = 445 votes.

 

To check the answer, make sure that 65 and 445 add up to 510.

 

Dan