Question

The city's water company charges a fee of \$20 a month in addition to \$0.25 per gallon used. Using the function $c = 0.25x + 20$, where $c$ is the total cost per month for water services and [tex]$x$[/tex] is gallons used, which of the following points on the graph accurately represents a monthly usage of 1,200 gallons?
A. (1,200, 320)
B. (1,200, 300)
C. (1,200, -180)
D. (320, 1,200)

Answer 1

To find the total cost \( c \) per month for water services when the monthly usage is 1,200 gallons, we can plug in \( x = 1200 \) into the function \( c = 0.25x + 20 \).

The calculation will be as follows:

\[
c = 0.25(1200) + 20
\]

First, calculate \( 0.25 \times 1200 \):

\[
0.25 \times 1200 = 300
\]

Next, add the fixed fee of \( 20 \):

\[
c = 300 + 20 = 320
\]

Therefore, when the water usage is 1,200 gallons, the total cost is \( 320 \).

This gives us the point \( (1200, 320) \).

Given the options:
A. \( (1,200, 320) \)
B. \( (1,200, 300) \)
C. \( (1,200, -180) \)
D. \( (320, 1,200) \)

The point that accurately represents a monthly usage of 1,200 gallons is:

**A. \( (1,200, 320) \)**