From the image, I see questions related to algebraic structures, primarily focusing on setting up and solving equations for the cost of renting vans from two different companies (Company A and Company B). Let me walk through each part as seen in the image and guide you with the solutions.

Questions Summary:

1. Company A charges $39.95 per day plus $0.79 per mile.
2. Company B charges $59.95 per day plus $0.29 per mile.

You are tasked with writing equations that represent the total daily rental costs for both companies, evaluating those equations for specific values of miles driven, and determining when the costs are equal.

Let's address the individual questions:

a) Write two equations:

Let $m$ represent the number of miles driven, and let $A$ and $B$ represent the total daily rental costs for Company A and Company B, respectively.

• For Company A: $A = 39.95 + 0.79m$
• For Company B: $B = 59.95 + 0.29m$

b) Evaluate the first equation if $m = 37$:

Using the equation for Company A: $A = 39.95 + 0.79(37)$ Solving this: $A = 39.95 + 29.23 = 69.18$ The total cost for Company A when driving 37 miles is $69.18.

c) Evaluate the second equation if $m = 42$:

Using the equation for Company B: $B = 59.95 + 0.29(42)$ Solving this: $B = 59.95 + 12.18 = 72.13$ The total cost for Company B when driving 42 miles is **$