Answer:
[tex]c(x)=150+16.52x[/tex]
Explanation:
The total cost is comprised of three costs, namely the flat fee for the room rental ($150), the charge person for the Italian buffet ($14 per person), and the tip (18% added to the cost of the food). With this you can build your equation:
[tex]Total\text{ }cost=$150+$14x+18\%\times (14x)[/tex]
Where x respresents the number of people attending the party.
Convert 18% to its decimal form, which is 0.18 and simplify the equation:
[tex]Total\text{ }cost=$150+$14x+0.18\times (14x)=150+14x+2.52x\\ \\ Total\text{ }cost=150+16.52x[/tex]
Hence, calling the function c(x), it is:
[tex]c(x)=150+16.52x[/tex], with x being the number of people attending the party, and c(x) the cost in dollars.
The function which representing the total cost of party is [tex]150+16.52x[/tex]
Let us consider that number of people who attending part be x.
The room rental amount is $150.
The charge of the Italian buffet for per person = $14
For x number of people [tex]=14x[/tex]
Since, 18% tip added to the cost of the food.
Tip cost [tex]=14x*\frac{18}{100} =2.52x[/tex]
Total cost of the party [tex]=150+14x+2.52x=150+16.52x[/tex]
Learn more about the function here:
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