Two friends are planning a vacation. They are deciding between Arizona and New York. The airfare for Arizona is $95 per person and the airfare for New York is $150 per person. The hotel in New York is $120 per night and the hotel in Arizona is $150 per night. They would share a hotel room. After how many nights would the trip's cost be equal to each other?

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boffeemadrid boffeemadrid · Answer 1 · 2021-01-09T18:05:19+01:00

Answer:

7

Step-by-step explanation:

Let number of nights spent in both the locations be [tex]x[/tex]

Airfare for Arizona for 2 persons for two way journey = [tex]95\times 4=\$380[/tex]

Airfare for New York for 2 persons for two way journey = [tex]150\times 4=\$600[/tex]

Cost of night spent in Arizona = [tex]150x[/tex]

Cost of night spent in New York = [tex]120x[/tex]

Cost of going and coming back from Arizona = [tex]380+150x[/tex]

Cost of going and coming back from New York = [tex]600+120x[/tex]

Now the costs should be equal so

[tex]380+150x=600+120x\\\Rightarrow 150x-120x=600-380\\\Rightarrow x=\dfrac{220}{30}\\\Rightarrow x=7.33\ \text{nights}[/tex]

The number of nights is approximately 7 at which the cost of the trip becomes equal.