SOLUTION: during one month, a homeowner used 400 units of electricity and 150 units of gas for a total cost of $76.50. the next month, 450 units of electricity and 100 units of gas were used

Question 242723: during one month, a homeowner used 400 units of electricity and 150 units of gas for a total cost of $76.50. the next month, 450 units of electricity and 100 units of gas were used for a total cost of $78.50. find the cost per unit of electricity.
Answer by blwinbbbles(106) (Show Source): You can put this solution on YOUR website!
so write down what we know:
e = electric g = gas
We know that in one month: (1)400e + 150g = $76.50
and in the next month: (2)450e + 100g = $78.50
So we need to use elimination to solve this problem.
Let's eliminate the g..to do that we need to make the units of g's exact opposites, so that when we add the equations we will get zero for the g.
The easiest way to do that is multiple equation 2 by -1.5
this will give us:
-675e - 150g = -117.75
now add this equation to equation 1
400e + 150g = $76.50
-675e - 150g = -$117.50
the answer is -275e = -$41.25
divide both sides by -275 and you get e = $0.15
So one unit of electricity is $0.15

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