In a town election, the winning candidate had 220 more votes
than the loser. If 810 votes were cast in all, how many votes did each candidate receive?
would the formula i need to solve this problem
x+y+220=810
y=x-220
The equations are not correct. Close, but you made a small error that would throw everything off.
You have:
x+y+220 = 810
If "x" represents one person's amount of votes and "y" equals the other person's amount of votes, you would not add ANOTHER 220 to see how many votes there were. If we said "Larry has 1 more apple than Matt and together, they have 5. How many apples does each person have?" You would not add the number I have plus the number you have plus another 5 (or we would have 10 apples since 5+5=10). Same idea here, just with bigger numbers. :)
y=x-220. Could work depending on how you define your variables. I think...haven't tried it yet and it's late here (1:15 AM)and I can't focus correctly because I'm tired. But look how I declared them below:
x = winner
y = loser
The winner (y) had 220 more votes than the loser (x) So just put that into numbers and variables as it's written:
y= 220 + x
If 810 votes were cast in all...
So if I add the number of the winner's votes and the number of the loser's votes, I have 810 votes all together:
x+y = 810
Now, you know what "y" equals (220 + x) Switch out the "y" for that and you're on your way :)
Matt
In the given town election, we have two candidates - the winner and the loser. Let's assign variables to represent the number of votes received by each candidate.
Let x represent the number of votes received by the winner.
Let y represent the number of votes received by the loser.
According to the information given, the winning candidate had 220 more votes than the loser. This can be expressed as:
x = y + 220
Additionally, we are told that a total of 810 votes were cast in all. This can be represented by the equation:
x + y = 810
Now, we have a system of equations that we can solve simultaneously to find the values of x and y.
Substitute the value of x from the first equation into the second equation:
(y + 220) + y = 810
Simplify the equation:
2y + 220 = 810
Subtract 220 from both sides:
2y = 810 - 220
2y = 590
Divide both sides by 2:
y = 590 / 2
y = 295
Now, substitute the value of y back into the first equation to find x:
x = 295 + 220
x = 515
Therefore, the winning candidate received 515 votes and the loser received 295 votes.