Question

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?

Answer 1

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.

$\Rightarrow3x+4y=675$  ......(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,  $x=\frac{675-4y}{3}$

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

solve,

$\Rightarrow 4\times(675-4y)+5y\times3=875\times3$  (Taking LCM)

$\Rightarrow2700-16y+15y=2625$

$\Rightarrow y=2700-2625=75$

Now, put value of $y=75$ in value of  $x=\frac{675-4y}{3}$

$\Rightarrow x=\frac{675-4(75)}{3}$

$\Rightarrow x=\frac{675-300}{3}$

$\Rightarrow x=\frac{375}{3}$

$\Rightarrow x=125$

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

Answer 2

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.