Question

mia has joined the frequent coffee buyer program with a local cafe. the program costs $15 per month which allows her to get a discounted coffee price of $1.00 per cup. answer the questions below regarding the relationship between the number of cups of coffee purchased and the total monthly cost.

answer attempt 1 out of 2

the independent variable x represents the , and the dependent variable is the , because the depends on the .

a function relating these variables is h(x) =

so h(17) = , meaning 17

Explanation:

Step1: Identify Variables

The independent variable \( x \) represents the number of cups of coffee purchased (since it's the quantity we can choose freely). The dependent variable is the total monthly cost (as it depends on the number of cups bought). The total monthly cost depends on the number of cups of coffee purchased.

Step2: Formulate the Function

The monthly program cost is $15 (fixed) and each cup costs $1. So the total cost \( H(x) \) is the fixed cost plus the cost per cup times the number of cups. Thus, \( H(x) = 15 + 1 \cdot x = x + 15 \).

Step3: Calculate \( H(17) \)

Substitute \( x = 17 \) into \( H(x) \): \( H(17) = 17 + 15 = 32 \). This means 17 cups of coffee will cost a total of $32 for the month.

Answer:

• The independent variable \( x \) represents the number of cups of coffee purchased, and the dependent variable is the total monthly cost, because the total monthly cost depends on the number of cups of coffee purchased.
• A function relating these variables is \( H(x) = x + 15 \).
• So \( H(17) = 32 \), meaning 17 cups of coffee will cost a total of $32 for the month.