Help on algebra question

Question

The skateboard rental company charges a set fee plus a daily rate to rent a skateboard it cost $5 to rent a regular skateboard for the first day and $13 to rent the same skateboard for 3 days. Which function models the given information?

Answer 1

3 days = 2 additional days and costs $13 - $5 = $8 extra.

Cost per additional day = $8/2 = $4.

Let d = days and c = charge.

Alternative 1:

cost structure = $5 plus $4 for each additional day

c = 5 + 4(d -1) where d >= 1

check:

d = 1: 5 + 4(1 - 1) = 5

d = 3: 5 = 4(3 - 1) = 13

Alternative 2:

simplify equation:

c = 5 + 4(d -1)

c = 5 + 4d - 4

c = 1 + 4d where d >= 1

cost structure = $1 fee plus $4 per day including first day

check:

d = 1: 1 + 4x1 = 5

d = 3: 1 + 4x3 = 13

Answer 2

$5 is the set fee

$13 is the daily rate for the maximum of 3 days so the function is 13x +5 is less than or equal to 3.