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 $37.56 , and the cost for using 39 HCF is $74.31. What is the cost for using 32 HCF of water?

Answer 1

$62.06

Explanation:

We use the given information as two points on a line.

Then we find the equation of the line.

Finally, we find the cost of 32 HCF of water.

Let y = cost.

Let x = number of HCF.

18 HCF cost $37.56. This gives us ordered pair (18, 37.56).

39 HCF cost $74.31. This gives us ordered pair (39, 74.31)

y = mx + b

m = slope = (74.31 - 37.56)/(39 - 18) = 36.75/21 = 1.75

Now we use point (18, 37.56).

37.56 = (1.75)(18) + b

b = 6.06

The equation of the cost is

y = 1.75x + 6.06

For 32 HCF, x = 32.

The cost, y is

y = 1.75x + 6.06

y = 1.75 × 32 + 6.06

y = 62.06

Answer: $62.06