Question

A city parking garage charges a flat rate of $5.00 for parking and $2.00 per hour parked Part A: write an equation with two variables that gives the total charge in terms of hours parked.Part B: create and insert a graph of your equation. you may snip the coordinate plane provided or create one of your own Part C: if Parrish has $20, how long can he park in the garage? Include evidence to support your solution (show and/or explain work) Write your answer in a complete sentence

Answer 1

ANSWER and EXPLANATION

We have that the city parking garage charges a flat rate (constant rate) of $5.00 for parking and $2.00 per hour parked.

A) Let the amount of hours parked be h.

Let the total cost of parking be C.

This means that C, the total cost of parking, is equal to the sum of the flat rate and the charges for the number of hours parked.

Therefore, we have that:

C = 2 * h + 5

=> C = 2h + 5

B) To plot a graph for this equation, we have to find at least two points that satisfy the equation, i.e. (h1, C1) and (h2, C2)

Let us find the values of C when h is 2 and when h is 5, that is the total cost of parking after 2 hours and after 5 hours.

When h = 2 hours:

=> C = 2(2) + 5 = 4 + 5

C = $9

When h = 5 hours:

C = 2(5) + 5 = 10 + 5

C = $15

Now, we can plot the graph using h values on the x axis and C values on the y axis.

We will use the two points (2, 9) and (5, 15)

That is the graph of the equation.

C) There are two ways to solve this:

=> Check for the value of h when C is $20 on the graph.

=> Find the value of h when C is $20 from the equation.

Let us use the equation. We have that:

C = 2h + 5

=> 20 = 2h + 5

Collect like terms:

=> 20 - 5 = 2h

15 = 2h

Divide both sides by 2:

h = 15 / 2

h = 7.5 hours

To confirm, we can check the graph for h when C is 20, we will find that the value is the same as the solution of the equation.

The complete sentence:

If Parrish has $20, it means that he can park for 7.5 hours (or 7 and a half hours).