The function c=180n+250 represents the total lodging cost c (in dollars) for a stay at a vacation destination of n nights.

You have budgeted $900 for lodging so how many nights can you stay at you vacation destination? Round answer down!

n=?

Given:

The function for the total lodging cost c (in dollars) for a stay at a vacation destination of n nights is

[tex]c=180n+250[/tex]

Budget = $900

To find:

The number of nights you can stay at you vacation destination.

Solution:

Since, budget is $900, therefore, the cost must be less than or equal to $900.

[tex]c\leq 900[/tex]

[tex]180n+250\leq 900[/tex]

[tex]180n\leq 900-250[/tex]

[tex]180n\leq 650[/tex]

Divide both sides by 180.

[tex]n\leq \dfrac{650}{180}[/tex]

[tex]n\leq 3.611[/tex]

Number of nights must be a whole number. So, greatest whole value of n is 3.

Therefore, you can stay 3 nights, i.e., n=3.

Number of nights he stay is 3.6

Given that;

Cost function

C = 180n + 250

Total cost = $900

Number of nights

Cost function

C = 180n + 250

Total cost = $900

So,

900 = 180n +250

180n = 650

n = 3.6 nights (Approx.)

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