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?

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.

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DodieZollner DodieZollner · Answer 2 · 2019-01-03T11:37:11+01:00

Answer:

The cost of one night at the hotel is $125

Step-by-step 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.

[tex]\Rightarrow3x+4y=675[/tex] ......(1)

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

[tex]\Rightarrow4x+5y=875[/tex] .......(2)

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

From (1) take the value of x, [tex]x=\frac{675-4y}{3}[/tex]

then put in equation (2) [tex]4\times\frac{675-4y}{3}+5y=875[/tex]

solve,

[tex]\Rightarrow 4\times(675-4y)+5y\times3=875\times3[/tex] (Taking LCM)

[tex]\Rightarrow2700-16y+15y=2625[/tex]

[tex]\Rightarrow y=2700-2625=75[/tex]

Now, put value of [tex]y=75[/tex] in value of [tex]x=\frac{675-4y}{3}[/tex]

[tex]\Rightarrow x=\frac{675-4(75)}{3}[/tex]

[tex]\Rightarrow x=\frac{675-300}{3}[/tex]

[tex]\Rightarrow x=\frac{375}{3}[/tex]

[tex]\Rightarrow x=125[/tex]

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