Question

Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount monthly plus a charge for each cubic foot of water used. A household using 1700 cubic feet was billed $126, while one using 2500 cubic feet was billed $150. Write an equation for the total cost of a resident's water as a function of cubic feet of water used.

Answer 1

To derive the total cost equation for the water bill, a system of linear equations was solved to find the fixed charge and the variable rate per cubic foot. The cost function is C(x) = 75 + 0.03x, where C represents the total cost and x represents cubic feet of water used.

Step-by-step explanation:

To find the equation that represents the total cost of a resident's water bill as a function of the cubic feet of water used, we first need to establish the fixed charge and the variable charge per cubic foot. We do this by setting up a system of linear equations based on the information provided about the two households.

Let F be the fixed monthly charge and V be the variable charge per cubic foot. We can set up two equations based on the given information:

1. For the household using 1700 cubic feet with a bill of $126: F + 1700V = 126
2. For the household using 2500 cubic feet with a bill of $150: F + 2500V = 150

Subtracting the first equation from the second gives us:

800V = 24

Dividing both sides by 800, we find:

V = 0.03

Now, we plug the value of V back into the first equation to find F:

F + 1700(0.03) = 126

F + 51 = 126

F = 126 - 51

F = 75

Therefore, the equation for the total cost C, in dollars, as a function of x, the cubic feet of water used, is:

C(x) = 75 + 0.03x

Answer 2

Cost function C(x) where x is the cubic feet of water used.

`C(x) = 75 + 0.03x`

Step-by-step explanation:

We are given the following in the question:

The municipal water supply are billed a fixed amount monthly plus a charge for each cubic foot of water used.

Let x be the fixed amount and y be the cost for each cubic foot of water used.

A household using 1700 cubic feet was billed $126.

Thus, we can write:

`x + 1700y = 126`

A household using 2500 cubic feet was billed $150.

`x + 2500y = 150`

Solving the two equation by eliminating x by subtracting the equations, we get,

`x+2500y-(x + 1700y) = 150-126\\800y = 24\\\\y =(24)/(800) = 0.03\\\\x+1700(0.03) = 126\\\Rightarrow x = 126-(1700)(0.03) = 75`

Thus, the fixed cost is $75 and the cost per cubic foot of water is $0.03

Cost function can be written as:

`C(x) = 75 + 0.03x`

where x is the cubic feet of water used.