Question

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)

Answer 1

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: $(400)(0.5)=200$$. 

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 $x$ represent the number of days of Arnold's business trip:
$y=40x+200$
where
$y$ is the amount the company will reimburse Arnold after $x$ days.
$x$ is the number of days.

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

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