Help with creating an expression

[JamesM]

I need to create an expression for the following situation:

I'm trying to determine the cost of a party. The cost is $200 for up to 20 people and then $5/person after 20. My expression to determine the cost is 200 + ((x-20)*5). This works as long as x is 20 or above. If x is less than 20, the expression should evaluate to $200, but I'm not sure how to show this.

Thanks for any suggestions.

JM

 

[NinjaKiwi]

I don't quite understand the question, but isn't it just f(x)=200+5x, where 200 is the base cost no matter what and x is number of people after 20 and f(x) is the cost?

So if 10 people arrive after the 20, it's f(10)=200+5*10=250

 

[JamesM]

I don't quite understand the question, but isn't it just f(x)=200+5x, where 200 is the base cost no matter what and x is number of people after 20 and f(x) is the cost?

So if 10 people arrive after the 20, it's f(10)=200+5*10=250

But what if only 10 people arrive, not 30(or 10 after the 20)? My equation would still give an answer of 250.

 

[NinjaKiwi]

Then sir, you have a bigger problem than money.

But isn't the base cost 200 dollars? no matter if 1 or 19 arrive, you're still going to have to pay 200 dollars? and after that 5 dollars per participant?

 

[JamesM]

\(\displaystyle If\ x\leq 20, C = 200.\)

\(\displaystyle If\ x > 20, C = 200 + 5(x - 20).\)

Your cost function is defined "piecewise."

This is what I was thinking. There is no way to express it with just one equation.