Arnold's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $40 a day for food and lodging and $0.50 for each mile traveled. Arnold drove 400 miles and was reimbursed $2600. Part A: Create an equation that will determine the number of days x on the trip (3 points) Part B: Solve this equation justifying each step with an algebraic property of equality. (6 points) Part C: How many days did Arnold spend on this trip? (1 points)

We know for the problem that Arnold drove 400 miles during his business trip, and the cost of each mile is $0.50, so the total cost of the miles the company will reimburse is: [tex](400)(0.5)=200[/tex]$.

Part A. We now know that the total cost of the miles the company have to pay to Arnold is $200. We also know the company pays him $40 a day for food and lodging. So let [tex]x[/tex] represent the number of days of Arnold's business trip:
[tex]y=40x+200[/tex]
where
[tex]y[/tex] is the amount the company will reimburse Arnold after [tex]x[/tex] days.
[tex]x[/tex] is the number of days.

Part B. We know that the amount the company will reimburse Arnold is $2600, so [tex]y=2600[/tex]. Lets replace that value in our equation and solve for [tex]x[/tex] to find the number of days:
[tex]y=40x+200[/tex]
[tex]2600=40x+200[/tex]
The first thing we are going to do to solve our equation is subtract 200 to both sides using the subtraction property of equality:
[tex]2600-200=40x+200-200[/tex]
[tex]2400=40x[/tex]
Next, we are going to divide both sides of the equation by 40, using the division property of equality, to find the value of [tex]x[/tex]:
[tex] \frac{2400}{40} = \frac{40x}{40} [/tex]
[tex]60=x[/tex]
Finally, we can use the reflexive property of equality to get:
[tex]x=60[/tex]

Part C. We can conclude that Arnold spend 60 days in his business trip.