pre-calc: find per-cubic-foot charge, total cost fcn, usage

[kalpana]

hi i really need help in this i already have solved the question a) but i m not able to find the other two plz help.

Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $74, while one using 1600 cubic feet was billed $111.

(a) What is the exact charge per cubic foot?
$

(b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used.
C(w) =

(c) How many cubic feet of water used would lead to a bill of $155? Give your answer to the nearest cubic foot.
ft3

 

[wjm11]

hi i really need help in this i already have solved the question a) but i m not able to find the other two plz help.

Residents of the town of Maple Grove who are connected to the municipal water supply are billed a fixed amount yearly plus a charge for each cubic foot of water used. A household using 1000 cubic feet was billed $74, while one using 1600 cubic feet was billed $111.

(a) What is the exact charge per cubic foot?
$

(b) Write an exact equation for C, the total cost, of a resident's water as a function of w, cubic feet of water used.
C(w) =

(c) How many cubic feet of water used would lead to a bill of $155? Give your answer to the nearest cubic foot.
ft3

Hello, Kalpana,

You say you have solved “a)”, but you have not demonstrated that. What did you get for a)?

Let’s look at the problem this way: we’ve been given two data points, (1000, 74) and (1600, 111). Plot these on a graph to see what’s going on, with cubic feet on the x-axis and Cost in dollars on the y-axis.

These two points define a line. The slope of the line is your rate (in this case, the cost per cubic foot). Just use the two data points to find the equation of the line.

What does the y-intercept on the graph represent? Think about it: how many cubic feet have been used at this point? None, right? This is the “fixed amount yearly” that everyone must pay regardless of how much water they use.

Now that you have the equation, you can plug in any amount of water used and find out the cost – or vice versa.