logo for solving-math-problems.com
leftimage for solving-math-problems.com

Algebra word problem - votes received

by Thomas












































In a recent school election, 980 votes were cast. The winner received 372 votes more than the loser. How
many votes did each of the two candidates receive?

Comments for Algebra word problem - votes received

Click here to add your own comments

Mar 16, 2011
Algebra Word Problem - Votes Received
by: Staff


The question:

by Thomas

In a recent school election, 980 votes were cast. The winner received 372 votes more than the loser. How many votes did each of the two candidates receive?


The answer:

Definitions:

T = total votes cast = 980 votes

x = votes cast for candidate 1, the winning candidate

y = votes cast for candidate 2


The total number of votes equals the votes cast for candidate 1 plus the votes cast for candidate 2.

T = x + y

980 = x + y


The winning candidate (candidate 1) received 372 more votes than the losing candidate (candidate 2).

372 = x – y

We now have two equations with two unknowns:

980 = x + y

372 = x – y

To solve for x (candidate 1, the winning candidate), add the two equations:

980 = x + y

372 = x – y
--------------
980 + 372 = x + y + x - y

980 + 372 = x + y + x - y

1352 = x + y + x - y

1352 = x + x + y - y

1352 = 2x + 0

1352 = 2x

Divide each side of the equation by 2

1352/2 = 2x/2

676 = 2x/2

676 = x*(2/2)

676 = x*1

676 = x (the winning candidate received 676 votes)

To solve for y (candidate 2, the losing candidate), substitute 676 for x in the first equation:

980 = x + y

980 = 676 + y

Subtract 676 from each side of the equation:

980 - 676 = 676 - 676 + y

304 = 676 - 676 + y

304 = 0 + y

304 = y (the losing candidate received 304 votes)


The final answer is: winning candidate received 676 votes, losing candidate received 304 votes.



Thanks for writing.


Staff
www.solving-math-problems.com


Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Math Questions & Comments - 01.



Copyright © 2008-2015. All rights reserved. Solving-Math-Problems.com