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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?

User Cela
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2 Answers

4 votes

Answer:

The cost of one night at the hotel is $125

Explanation:

Let the cost of each night spend in hotel is = $x

Let the cost of each day of car rented = $y

Cannor spent 3 nights at a hotel and rented a car for 4 days paid $675.


\Rightarrow3x+4y=675 ......(1)

Jillian also spent 4 nights in same hotel and rented a car for 5 days paid $875.


\Rightarrow4x+5y=875 .......(2)

Now, we solve equation (1) and (2) by substitution method

From (1) take the value of x,
x=(675-4y)/(3)

then put in equation (2)
4*(675-4y)/(3)+5y=875

solve,


\Rightarrow 4*(675-4y)+5y*3=875*3 (Taking LCM)


\Rightarrow2700-16y+15y=2625


\Rightarrow y=2700-2625=75

Now, put value of
y=75 in value of
x=(675-4y)/(3)


\Rightarrow x=(675-4(75))/(3)


\Rightarrow x=(675-300)/(3)


\Rightarrow x=(375)/(3)


\Rightarrow x=125

Therefore, the cost of one night at the hotel is $125


User Beije
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7.8k points
2 votes
The answer for the question in problem would be $125 is the price of hotel per night. This is computed by establishing the equations from the given statements, 3x + 4y = 625 and 4x +5y = 875. And by substitution you would get the answer of 125 as the price per night n the hotel and 75 per day for the rental of car.
User Jose Paez
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7.6k points
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