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 18 HCF of water is $36.15, and the cost for using 46HCF is $85.15. What is the cost for using 34HCF of water?

Answer 1

The cost for using 34HCF of water, based on the linear relationship between cost and water use detailed in the student's question, is calculated to be $63.52.

Step-by-step explanation:

The student's question requires finding the cost for using 34HCF of water given a linear relationship between water usage and cost. We know the cost for 18HCF is $36.15 and for 46HCF is $85.15. To find the cost for 34HCF, we first need to determine the cost per HCF, and then apply it to 34HCF.

First, we calculate the slope (cost per HCF) using the given points (18, 36.15) and (46, 85.15):

Slope = (Change in cost) / (Change in HCF)
Slope = (85.15 - 36.15) / (46 - 18)
Slope = 48.00 / 28
Slope = $1.7143 per HCF

Next, we use one of the points and the slope to create the equation y = mx + b. Using the point (18, 36.15):
36.15 = 1.7143(18) + b
b = 36.15 - (1.7143 * 18)
b = 5.34 (the fixed monthly charge)

Now, we can find the cost for using 34HCF:
Cost = 1.7143(34) + 5.34
Cost = $58.18 + 5.34
Cost = $63.52