Brianna went to los angeles for a 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?

$150 per night

Use a system of equations using x (cost of hotel) and y (cost of 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

Since there are no images given for the problem, i will define the parabola. a parabola is an open curve that is formed when a cone is sliced parallel to the side of it. the key aspects of a parabola when it is graphed looks like a curve that opens upward, downward, leftward or rightward. it has a latus rectum which is the length of the ends of a curved line. the directrix is the distance between the vertex of a parabola and the line. the vertex is the point where the curve ends.