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 24 HCF of water is $38.10, and the cost for using 55 HCF is $79.95. What is the cost for using 29 HCF of water?​

Answer 1

The cost for using 29 HCF of water is $38.95.

Explanation:

Let C be the monthly cost in dollars, and let x be the amount of water used in hundreds of cubic feet (HCF). We can write a linear equation in the form:

C = mx + b

where m is the slope (the rate of change of cost with respect to water use) and b is the y-intercept (the fixed cost component).

We are given two points on the line: (24, 38.10) and (55, 79.95). Using these points, we can find the slope:

m = (79.95 - 38.10) / (55 - 24)

= 1.49

Now we can use the point-slope form of a line to write the equation:

C - 38.10 = 1.49(x - 24)

Simplifying:

C = 1.49x - 7.26

To find the cost for using 29 HCF of water, we substitute x = 29 into the equation:

C = 1.49(29) - 7.26

= 38.95

Therefore, the cost for using 29 HCF of water is $38.95.