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What are are the variable, equation, and inequality for this question?

A rental car company charges $50 plus $0.20 per mile to rent a car. Marissa must spend less than $184.60. How many miles can Marissa drive the car?

1 answer

To analyze the situation, we need to identify the variable, formulate an equation, and establish an inequality based on the information provided.

Variable:

Let's define the variable:

  • Let \( x \) represent the number of miles Marissa drives the car.

Equation:

The total cost \( C \) for renting the car can be expressed as: \[ C = 50 + 0.20x \] where:

  • \( 50 \) is the fixed rental fee,
  • \( 0.20x \) is the cost for driving \( x \) miles.

Inequality:

According to the problem, Marissa wants to spend less than $184.60. Therefore, we can set up the following inequality: \[ 50 + 0.20x < 184.60 \]

Summary:

  • Variable: \( x \) (number of miles driven)
  • Equation: \( C = 50 + 0.20x \)
  • Inequality: \( 50 + 0.20x < 184.60 \)

From the inequality, we can solve for \( x \) to determine the maximum number of miles Marissa can drive.