A rental car company is running two specials. Customers can pay $37 to rent a compact car for the first day plus $8 for each additional day, or they can rent the same car for $31 the first day and $9 for every additional day beyond that. Greg notices that, given the number of additional days he wants to rent the car for, the two specials are equivalent. How much would Greg pay in total? How many additional days does Greg want?
Let's say Greg wants to rent the car for $d$ additional days.
With the first special, Greg would pay $37 + 8d$ dollars.
With the second special, Greg would pay $31 + 9(d-1)$ dollars.
Since the two specials are equivalent, we can set up the following equation:
$37 + 8d = 31 + 9(d-1)$
Expanding the equation, we get:
$37 + 8d = 31 + 9d - 9$
Simplifying, we have:
$37 - 31 + 9 = 9d - 8d$
$15 = d$
So Greg wants to rent the car for 15 additional days.
Now we can calculate the total cost by substituting $d = 15$ into either equation. Let's use the second equation:
Total cost = $31 + 9(15-1)$
Total cost = $31 + 9 \times 14$
Total cost = $31 + 126$
Total cost = $157$
Greg would pay $157 in total. He wants to rent the car for 15 additional days.