Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

While visiting Cedarburg, Darren can pay a flat rate of $10 for parking or $2 per hour. For the length of time that Darren wants to park in Cedarburg, the two options are actually equivalent in terms of cost. How much will Darren pay? For how long does Darren want to park?

Darren will pay $
for
hours of parking.

Answer 1

To describe the situation with a system of equations, we can set up the following:

Let \( h \) represent the number of hours Darren parks.

The cost of parking for the flat rate option is: \[ C_1 = 10 \]

The cost of parking for the hourly rate option is: \[ C_2 = 2h \]

Since the two options are equivalent in terms of cost, we can set the two equations equal to each other: \[ 10 = 2h \]

Now, we can solve for \( h \):

1. Divide both sides by 2: \[ 5 = h \]

So, Darren wants to park for \( 5 \) hours.

Now we can find how much Darren will pay using either cost equation. Using the flat rate option: \[ C_1 = 10 \]

Or using the hourly rate option: \[ C_2 = 2h = 2(5) = 10 \]

Thus, it doesn't matter which option he chooses; the cost is the same.

Concluding the answers: Darren will pay $10 for 5 hours of parking.

Final fill in the blanks: Darren will pay $10 for 5 hours of parking.