Question

Brianna went to Los Angeles for vacation. She spent 5 nights at a hotel and rented a car for 6 days. Justin stayed at the same hotel, but spent 7 nights and rented a car for 8 days from the same company. If Brianna paid $1170 and Justin paid $1610, how much did one night at the hotel cost?

Answer 1

Use a system of equations where x is the cost per night of the hotel and y is the cost per day for renting a car:

5x + 6y = 1170
7x + 8y = 1610

Solve for y in one of the equations and then use substitution to solve for x in the other:

6y = 1170 - 5x
y = (-5/6)x + 195

7x + 8((-5/6)x + 195) = 1610
7x + (-20/3)x + 1560 = 1610
(1/3)x +1560 = 1610
(1/3)x = 50
x = $150 a night