In a special local election, one candidate received 288 votes less than twice the number of votes of the opponent. How many votes did each candidate receive if the total number of votes in the election is 136,395?
OC=2OP-288
OC+OP=136,395
I don't understand this equation that you have here?
Those equations are what the problem states, that is all. OC is the one candiadate, OP is the opposing candidate.
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To find the number of votes each candidate received, we can set up an equation based on the given information.
Let's say one candidate received x votes and the other candidate received y votes.
According to the given information, one candidate received 288 votes less than twice the number of votes of the opponent. So we can write the equation as:
x = 2y - 288
Also, the total number of votes in the election is 136,395. This means that the sum of the votes received by both candidates is equal to 136,395:
x + y = 136,395
Now we have a system of two equations:
x = 2y - 288
x + y = 136,395
We can solve this system of equations to find the values of x and y, which represent the number of votes each candidate received.
There are several methods to solve this system of equations, such as substitution or elimination. Let's use the elimination method to solve it.
First, let's multiply the second equation by 2 to eliminate the y term:
2(x + y) = 2(136,395)
2x + 2y = 272,790
Next, let's subtract the first equation from the second equation:
2x + 2y - (x) = 272,790 - (2y - 288)
2x + 2y - x = 272,790 - 2y + 288
x = 272,790 - 2y + 288
Simplifying the equation:
x = 272,790 - 2y + 288
x = 272,790 + 288 - 2y
x = 273,078 - 2y
Now we have an expression for x in terms of y.
Let's substitute this expression for x in the first equation:
273,078 - 2y = 2y - 288
Let's solve for y:
273,078 - 288 = 2y + 2y
272,790 = 4y
Dividing both sides by 4:
y = 272,790 / 4
y = 68,197.5
Since the number of votes cannot be in decimals, it means there was an error in the calculation. Please double-check the given information and recompute.