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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?
A) $75
B) $100
C) $125
D) $150

Respuesta :

Answer: option C is the correct answer

Step-by-step explanation:

Let x represent the cost of one night at the hotel.

Let y represent the cost of renting the car for one day.

Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. If Connor paid $675, it means that

3x + 4y = 675 - - - - - - - - - - - 1

Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Jillian paid $875, It means that

4x + 5y = 875 - - - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 3, it becomes

12x + 16y = 2700

12x + 15y = 2625

Subtracting, it becomes

y = 75

Substituting y = 75 into equation 1, it becomes

3x + 4 × 75 = 675

3x + 300 = 675

3x = 675 - 300 = 375

x = 375/3 = $125

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