Question

Francesca is planning to rent a van for her trip to Mt. Dora. Two of her friends reach rented the same type of van from the same car rental company last week. This is what they told her. Brynn:"The costt of my rental was $240. The company charged me a certain amount per day and a certain amount per mile. I had the rental for 5 days and I drove it 200 miles. Danielle: "The cost of my rental was only $100. I drove it for 100 miles and had it for two days." Francesca estimated her trip woul be 250 miles, and she would have the van for 4 days. Let C=Cost, M=miles, and d = days.
a. C=40.00m + .20d
b. C =40.00D + .20 M
c. C=20.00M + 40 D
d. C=20.00D + .40 M
b. How much would francescas estimated cost be based on the equation?

Answer 1

A) Let's call:
x = amount charged per day
y = amount charged per mile

According to Brynn you have: 5x + 200y = 240
According to Danielle: 2x + 100y = 100

You need to solve the system in order to find the amount charged:
$\left \{ {{5x + 200y = 240} \atop {2x + 100y = 100}} \right.$

Solve for x on the second equation:
x = (100 - 100y) / 2 = 50 - 50y

Substitute in the first equation and solve for y:
5(50 - 50y) + 200y = 240
250 - 250y + 200y = 240
-50y = -10
y = 1 / 5 = 0.20

Now substitute this value in the equation found for x:
x = (50 - 50·0.20) = 40

Therefore the cost for Francesca will be:
C = 40·D + 0.20·M

The correct answer is B)

B) In order to find the cost for 250 miles and 4 days, you need to substitute the numbers in the formula found in part A):
C = 40·D + 0.20·M
   = 40·4 + 0.20·250
   = 210$

The cost estimated for Francesca is 210$.