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$35.99, and the cost for using 45 HCF is $83.84. What is the cost for using 24 HCF of water?

Answer 1

Modelling it to linear equation

`\begin{gathered} y=mx+b \\ \text{where} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

Therefore,

`\begin{gathered} y=\cos t \\ x=\text{amount of water} \end{gathered}`

(16, 35.99)(45, 83.84)

`\begin{gathered} m=(83.84-35.99)/(45-16)=(47.85)/(29)=1.65 \\ y=1.65x+b \\ 35.99=1.65(16)+b \\ 35.99-26.4=b \\ b=9.59 \\ \\ y=1.65x+9.59 \end{gathered}`

let's find the cost for using 24 HCF water

`\begin{gathered} y=1.65(24)+9.59 \\ y=39.6+9.59 \\ y=49.19 \\ \cos t\text{ = \$49.19} \end{gathered}`