Question

example
the total cost of renting a tent is equal to a rental fee plus a cleaning fee of $10. write an equation with two variables that shows how to find the total cost of renting a tent based on the rental fee.
you can define variables and use them to write an equation that represents the relationship between the rental fee and the total cost.
r = rental fee in dollars
t = total cost in dollars
the total cost is equal to the rental fee plus $10.
t = r + 10
the equation t = r + 10 can be used to find the total cost of renting a tent.
1 which variable is the independent variable in the example? which is the dependent variable? explain how you know.

Explanation:

To determine independent and dependent variables, we analyze their relationship. The independent variable is not affected by other variables in the context, while the dependent variable depends on the independent one. In the equation \( t = r + 10 \), the rental fee (\( r \)) can be chosen freely (e.g., different tents may have different rental fees set by the provider), and the total cost (\( t \)) is calculated based on the rental fee (it changes as \( r \) changes). So \( r \) is independent, and \( t \) is dependent because \( t \)’s value relies on \( r \)’s value.

Answer:

Independent variable: \( r \) (rental fee in dollars) because the rental fee can be determined or chosen independently (e.g., set by the tent - renting service, and we can pick different values for it). Dependent variable: \( t \) (total cost in dollars) because the total cost depends on the rental fee (we calculate \( t \) using the value of \( r \) in the equation \( t=r + 10 \), so \( t \)’s value is determined by \( r \)’s value).