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 $35.31, and the cost for using 51 HCF is $586.46. What is the cost for using 47 HCF of water?

a) $779.13
b) $684.22
c) $699.99
d) $826.18

Answer 1

The cost for using 47 HCF of water is $416.64.

Step-by-step explanation:

To find the cost for using 47 HCF of water, we need to determine the equation for the linear function that represents the cost of water use. We can use the given information to form two equations and solve them simultaneously. Let's use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

From the given information, we have two points: (18, 35.31) and (51, 586.46).

Using these points, we can calculate the slope:

slope = (586.46 - 35.31) / (51 - 18) = 551.15 / 33

Now, we can use the point-slope form with one of the points to find the equation of the line:

y - 35.31 = (551.15 / 33)(x - 18)

Simplifying the equation:

y = (551.15 / 33)x - 50.6 + 35.31 = (551.15 / 33)x - 15.29

Substituting 47 for x, we can find the cost for using 47 HCF of water:

y = (551.15 / 33)(47) - 15.29

y = 9.19(47) - 15.29

y = 431.93 - 15.29

y = 416.64

Therefore, the cost for using 47 HCF of water is $416.64.