Which of the following equations could be used?

Question

Parking fees at the local garage is $9.00 per day; Patrons who use this service frequently are given the opportunity to purchase a monthly discount card for $28.00. With the discount card, the parking fee is reduced to $5.50 per day. If “r” represents the number of days the parking lot is used, which of the following equations could be used to calculate when the options would cost the same amount and for how many days the cost will be the same, no matter which option is chosen?

A. 9r = 28 + 5.5, 2 days

B. 9r = 28 + 5.5, 8 days

C. 9r + 5.5r = 28, 2 days

D. 9r + 5.5r = 28, 8 days

Answer 1

Hi Bran,

 

Let's begin by getting expressions in terms of r (number of days) for each cost option:

    Option #1 (cost without monthly pass):

        9r ($9 per day)

    Option #2 (cost with monthly pass):

        28 + 5.50r ($28 pass + $5.50 per day)

 

Now we will come up with the equation to solve for the number of days for which the money amounts for the two cost options will be the same:

    9r = 28 + 5.50r (equating the two cost options) 

 

We can now solve the equation for r (number of days):

    9r = 28 + 5.50r

    9r - 5.50r = 28

          3.50r = 28

                r = 8 (days)

 

We can now see which answer choice is correct based upon our answers for the equation and the number of days, which I will happily leave to you.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

 

Answer 2

For the first option

 

cost = 9r

 

For the second option

 

cost = 28 + 5.5r

 

Cost is equal when

 

9r = 28 + 5.5r

 

The closest is B, yet an "r" is missing.