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 1500 cubic feet was billed $80, while one using 2100 cubic feet was billed $92. Write an equation for the total cost of a resident's water as a function of cubic feet of water used.

Answer 1

A = 50 + 0.02x

Explanation:

Let the fixed amount be m

Let the charge for each cubic ft used be c

Let the amount of cubic ft of water used be x.

Let the total cost per month be A

Now, for the first household, they used 1500 cubic feet in a month and were billed $80.

This means, x = 1500 ft³ and A = $80

Since, we are told they are charged a fixed amount plus a fee per cubic ft consumed. We can say that;

m + cx = A

Thus,

m + 1500c = 80 - - - - (eq1)

For 2nd household:

They used 2100 cubic feet was billed $92.

Thus;

m + 2100c = 92 - - - - (eq 2)

Let's subtract eq1 from eq 2 to get;

2100c - 1500c = 92 - 80

600c = 12

c = 12/600

c = 0.02

Putting 0.02 for C in eq1 gives;

m + 1500(0.02) = 80

m + 30 = 80

m = 80 - 30

m = 50

From m + cx = A, we can say that;

50 + 0.02x = A