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 17 HCF of water is $37.62, and the cost for using 56 HCF is $94.17. What is the cost for using 38 HCF of water?

Answer 1

We have a situation where we are describing the cost of hundreds of cubic feet in a linear function.

we have the cost for 17 and 56 HCF, with this data we can get the equation of the linear function, and with it, we can find the cost of 38 HCF which is the question to answer.

For this, we use the equation for the line

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Where:

`\begin{gathered} (x_1,y_1)=(17,37.62) \\ (x_2,y_2)=(56,94.17) \end{gathered}`

Now, we replace and clear "y"

`\begin{gathered} y-37.62=(94.17-37.62)/(56-17)(x-17) \\ y-37.62=(56.55)/(39)(x-17) \\ y-37.62=1.45(x-17) \\ y-37.62=1.45x-24.65 \\ y=1.45x+37.62-24.65 \\ y=1.45x+12.97 \end{gathered}`

In conclusion, the equation of the linear function is:

`y=1.45x+12.97`

Finally, to find the cost of 38 HCF we take x=38

`\begin{gathered} x=38 \\ y=1.45\cdot(38)+12.97 \\ y=55.1+12.97 \\ y=68.07 \end{gathered}`

In conclusion, the cost for using 38 HCF of water is $68.07