In an election between two candidates, 530 votes were cast. If the winner received received 150 more votes than the loser, how many votes did the winner receive?
a. 380 votes
b. 680 votes
c. 340 votes
d. 190 votes
help? I got 415, but it's not an answer.
I don't know what you did with 530 and 150 to get 415.
530 - 150 = ?
x + x + 150 = 530 Winner - x + 150
Loser - x
2x = 530 - 150
x = ?
To solve this problem, we can set up a system of equations. Let's denote the number of votes the winner received as "W" and the number of votes the loser received as "L".
We know that the total number of votes cast is 530, so we can write the equation:
W + L = 530 ...(Equation 1)
We are also given that the winner received 150 more votes than the loser, which can be written as:
W = L + 150 ...(Equation 2)
Now, we can solve this system of equations to find the values of W and L.
Substitute the value of W in Equation 2 into Equation 1:
(L + 150) + L = 530
Combine like terms:
2L + 150 = 530
Subtract 150 from both sides of the equation:
2L = 530 - 150
2L = 380
Divide both sides of the equation by 2:
L = 380 / 2
L = 190
Now, substitute the value of L back into Equation 2 to find W:
W = 190 + 150
W = 340
Therefore, the winner received 340 votes.
Among the options given, the correct answer is c. 340 votes.