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

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

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.