Math about Pizza

Question

The pizza that costs $18 will be shared among a group of friends. Each friend contributes the same amount of money to pay for the pizza.

1. Write a function, C(x), that can be used to calculate the total amount of money that each friend will contribute if x number of friends split the pizza.
2. As x increases, what happens to the value of C(x)?
3. What is the domain of C(x)? What is the range of C(x)? Explain. 

Answer 1

Alright, Natalie, let's do this thing.

 

Let's say that 3 friends split the pizza.  Then each friend spend $18/3 = $6.  So, if there are x friends, they will each spend $18/x

 

C(x) = 18/x

 

What happens if more friends show up?  Common knowledge tells us each has to chip in less!  Also, we know that as a the denominator increases, the fraction gets smaller. 1/2 > 1/4, so 18/3 > 18/6.

 

The domain is the input, or how many friends show up.  We obviously can't have fewer than one, or no one orders the pizza!  We can have as many friends as we want, so x > 1.

 

The range is the output, or how much each pays.  The amount each pays has to be between 0 and $18, since no one can pay less than 0 and only one person may pay the whole thing, so our our range is 0 < y > 18.

 

Hope this helps!