Question

darell parks his car in a parking garage. the garage charges a certain amount for the first hour and an hourly rate for each additional hour. the total charge for 3 hours is $10.65. the total charge for 6 hours is $15.30. complete the equation that describes the relationship between the total charge, c, and the length of time in hours, h. write your answer using whole numbers or decimals rounded to the nearest hundredth. c = \square h + \square

Explanation:

Step1: Define variables and equations

Let the charge for the first hour be \( b \) (the y - intercept) and the hourly rate for each additional hour be \( m \) (the slope). The total charge \( C \) and time \( h \) have a linear relationship \( C=mh + b \).
For \( h = 3 \), \( C=10.65 \), so \( 10.65=3m + b \).
For \( h = 6 \), \( C = 15.30 \), so \( 15.30=6m + b \).

Step2: Solve for m

Subtract the first equation from the second equation:
\((6m + b)-(3m + b)=15.30 - 10.65\)
Simplify: \( 6m + b-3m - b=4.65\)
\( 3m=4.65\)
Divide both sides by 3: \( m=\frac{4.65}{3}=1.55\)

Step3: Solve for b

Substitute \( m = 1.55 \) into \( 10.65=3m + b \):
\( 10.65=3\times1.55 + b\)
\( 10.65 = 4.65 + b\)
Subtract 4.65 from both sides: \( b=10.65 - 4.65 = 6\)

Answer:

\( C = 1.55h+6 \)