Connor went to new york for vacation. he spent 3 nights at a hotel and rented a car for 4 days. jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. if connor paid $675 and jillian paid $875, how much did one night at the hotel cost? .

Let x = cost for a night.      y = cost to rent car for a day.

Connor = 3 nights and 4 days = 3x + 4y = 675

Jillian = 4 nights and 5 days = 4x + 5y = 875

3x + 4y = 675            Multiply by 5

4x + 5y = 875            Multiply by 4


5*3x + 5*4y = 5*675                     15x + 20y = 3375

4*4x + 4*5y = 4*875                      16x + 20y = 3500     

15x + 20y = 3375
-
16x + 20y = 3500


-x     + 0    =  -125
 
x = 125 

The cost per night is x, = $125