Hunter has joined the Frequent Coffee Buyer program with a local cafe. The program costs $15 per month which allows him to get a discounted coffee price of $3 per cup. Answer the questions below regarding the relationship between the of number of cups of coffee purchased and the total monthly cost.

Answer

Attempt 1 out of 2

The independent variable, *x*, represents the  total monthly costnumber of coffee cups purchased, and the dependent variable is the  number of coffee cups purchasedtotal monthly cost, because the  number of coffee cups purchasedtotal monthly cost *depends on* the  total monthly costnumber of coffee cups purchased.
A function relating these variables is D, left parenthesis, x, right parenthesis, equals*D*(*x*)= .
So D, left parenthesis, 18, right parenthesis, equals*D*(18)= , meaning 1818  dollars will be paid forcups of coffee will cost

Let’s break down the problem to correctly identify the independent and dependent variables, define the function, and interpret the result:

1. The **independent variable $ x $** represents the **number of coffee cups purchased** because it is the input value that you control.
2. The **dependent variable** is the **total monthly cost**, because the total cost depends on the number of coffee cups purchased.
3. A function relating these variables would be:
   \[
   D(x) = 15 + 3x
   \]
   where $ D(x) $ represents the total monthly cost in dollars, and $ x $ represents the number of coffee cups purchased.

4. To find the cost if Hunter buys 18 cups of coffee:
   \[
   D(18) = 15 + 3(18) = 15 + 54 = 69
   \]
   So, $ D(18) = 69 $, meaning if Hunter buys 18 cups of coffee, the total monthly cost will be $69.

Here’s how the filled-in statement should look:

The independent variable, $ x $, represents the **number of coffee cups purchased**, and the dependent variable is the **total monthly cost**, because the **total monthly cost** depends on the **number of coffee cups purchased**.

A function relating these variables is $ D(x) = 15 + 3x $.

So $ D(18) = 69 $, meaning **$69 will be paid for 18 cups of coffee**.

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Would you like more details or have any questions? Here are 5 related questions:

1. How would the function change if the membership fee increased to $20 per month?
2. What is the total cost if Hunter buys only 10 cups of coffee in a month?
3. How many cups of coffee would Hunter need to buy for the total cost to reach $90?
4. If Hunter buys no coffee at all, what is the fixed monthly cost?
5. How can you represent this relationship graphically?

**Tip:** Fixed costs (like the $15 membership fee) remain constant, while variable costs (like $3 per cup) change depending on the number of items purchased.

Explore how to calculate the total monthly cost for a coffee buyer program. Learn about the relationship between the number of coffee cups purchased and the total monthly cost with a detailed function analysis. Includes examples like determining the cost for specific numbers of coffee cups.

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