Math Problem Statement

The linear model c = 2.20 + 2m describes the cost of a cab ride, c, as a function of the number of miles traveled, m. How much will it cost to travel 16 miles in a cab?

Solution

The given linear model is:

c=2.20+2mc = 2.20 + 2m

where:

  • cc is the cost of the cab ride.
  • mm is the number of miles traveled.
  • The base fare is 2.202.20.
  • The cost per mile is 22.

To find the cost for m=16m = 16 miles:

c=2.20+2(16)c = 2.20 + 2(16)

c=2.20+32c = 2.20 + 32

c=34.20c = 34.20

Thus, the correct answer is $34.20$.

Would you like more details or another explanation?

Here are five related questions for further practice:

  1. What is the cost of a cab ride for 10 miles using the same model?
  2. How would the cost change if the price per mile increased to $2.50?
  3. If a ride costs $50.20, how many miles were traveled?
  4. What is the slope of the given linear function, and what does it represent?
  5. How would you represent this function graphically?

Tip: In linear equations, the slope represents the rate of change, while the y-intercept represents the starting value. 🚖

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Cost Functions
Algebra

Formulas

c = 2.20 + 2m

Theorems

Linear Functions
Slope-Intercept Form

Suitable Grade Level

Grades 7-9