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 20 HCF of water is $35.13 and the cost for using 33 HCF is $57.88.what is the cost for using 27 HCF of water?

Answer 1

Since the relationship is linear, we will solve it as follows:

*We are given two points, we will find the slope:

$m=\frac{57.88-35.13}{33-20}\Rightarrow m=\frac{7}{4}$

*Now, we replace this slope and one of the points in the following expression:

$y-y_1=m(x-x_1)$

Now, we replace:

$y-35.13=\frac{7}{4}(x-20)\Rightarrow y-35.13=\frac{7}{4}x-35$$\Rightarrow y=\frac{7}{4}x+0.13$

Now, we replace the 27 HCF in the expression and solve for the cost:

$y=\frac{7}{4}(27)+0.13\Rightarrow y=47.38$

So, the cost for 27 HCF is $47.38.