Math Problem Statement

You are asked to create two equations representing the total rental cost from two companies, A and B, based on the number of miles driven. Company A charges $399.95 per day plus $0.79 per mile, and Company B charges $359.95 per day plus $0.92 per mile. You are also asked to evaluate the equations for m = 37 for Company A and m = 42 for Company B, and to solve for when the costs of both companies are equal.

Solution

The images you have uploaded seem to contain a word problem related to renting vans from two companies, A and B. From what I can see:

  1. Company A charges a base rate of $399.95 per day, plus $0.79 per mile.
  2. Company B charges a base rate of $359.95 per day, plus $0.92 per mile.

The problem requires creating equations to represent the total daily rental costs for each company based on the number of miles driven. The equations should look something like this:

  • Let A(m)A(m) represent the total cost for Company A, and B(m)B(m) represent the total cost for Company B, where mm is the number of miles driven.
    • For Company A: A(m)=399.95+0.79mA(m) = 399.95 + 0.79m
    • For Company B: B(m)=359.95+0.92mB(m) = 359.95 + 0.92m

Then, the following steps are requested:

Part b:

You are asked to evaluate these equations for specific values of mm:

  1. Evaluate A(37)A(37) (the first equation when m=37m = 37).
  2. Evaluate B(42)B(42) (the second equation when m=42m = 42).

Part d:

Set up a new equation to find when the cost of renting from Company A equals the cost of renting from Company B. That would involve solving A(m)=B(m)A(m) = B(m).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

A(m) = 399.95 + 0.79m (Cost for Company A)
B(m) = 359.95 + 0.92m (Cost for Company B)

Theorems

Linear Equation Solving

Suitable Grade Level

Grades 9-11