Finances. During one month, a homeowner used 500 units of electricity and 100 units of gas for a total cost of $352. The next month, 400 units of electricity and 150 units of gas were used for a total cost of $304. Find the cost per unit of gas. Please show the work. Thanks
Two equations; two unknowns.
500 x + 100 y = 352
400 x + 150 y = 304.
Solve for x and y.
y is the cost per unit of gas.
x is the cost per unit of electricity.
2000 x + 750 y = 1520
2000 x + 400 y = 1408
350 y = 112
y = $0.32 per unit
x = $0.64 per unit
To find the cost per unit of gas, we need to set up a system of equations using the given information.
Let's assume that the cost per unit of electricity is E and the cost per unit of gas is G.
From the first month:
The cost of electricity is 500 units * E.
The cost of gas is 100 units * G.
The total cost is $352.
So, the first equation is:
500E + 100G = 352.
From the second month:
The cost of electricity is 400 units * E.
The cost of gas is 150 units * G.
The total cost is $304.
So, the second equation is:
400E + 150G = 304.
We now have a system of two equations:
500E + 100G = 352 (equation 1)
400E + 150G = 304 (equation 2)
To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply equation 1 by 4 and equation 2 by 5 to make the coefficients of E in both equations equal:
2000E + 400G = 1408 (equation 3)
2000E + 750G = 1520 (equation 4)
Now, subtract equation 3 from equation 4 to eliminate E:
2000E + 750G - (2000E + 400G) = 1520 - 1408
2000E - 2000E + 750G - 400G = 112
350G = 112
Divide both sides of the equation by 350 to solve for G:
G = 112 / 350
Simplifying, we get:
G = 0.32
Therefore, the cost per unit of gas is $0.32.