Question

The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 16 HCF of water is $32.67, and the cost for using 30 HCF is $52.97. What is the cost for using 18 HCF of water?

Answer 1

Since it represents a linear function we can model the function like this:

`\begin{gathered} y=mx+b \\ where: \\ y=cost \\ x=amount_{\text{ }}of_{\text{ }}water \\ so: \\ (16,32.67) \\ 32.67=16m+b_{\text{ }}(1) \\ ----- \\ (30,52.97) \\ 52.97=30m+b_{\text{ }}(2) \\ \end{gathered}`

Using elimination:

`\begin{gathered} (2)-(1) \\ 52.97-32.67=30m-16m+b-b \\ 20.3=14m \\ m=(20.3)/(14) \\ m=1.45 \\ and \\ b=9.47 \end{gathered}`

Therefore, the function is given by:

`y=1.45x+9.47`

Evaluating for 18 HCF:

`\begin{gathered} y=1.45(18)+9.47 \\ y=26.1+9.47 \\ y=35.57 \\ \end{gathered}`

Answer:

The cost for using 18 HCF of water is $35.57