David's company reimburses his expenses on food, lodging, and conveyance during business trips. The company pays $60 a day for food and lodging and $0.65 for each mile traveled. David drove 600 miles and was reimbursed $3,390.

Part A: Create an equation that will determine the number of days \( x \) on the trip.

Part B: Solve this equation, justifying each step with an algebraic property of equality.

Part C: How many days did David spend on this trip?

Part A: the reimbursement for mileage would be 0.65 * 600 = 390.
Part B: x = (Total reimbursement - 390)/60
Part C: David spent 50 days on this trip

Part A: To create an equation that determines the number of days x on the trip, we need to consider the reimbursement for food and lodging as well as the reimbursement for mileage.
Let's assume that David spent x days on the trip. The reimbursement for food and lodging per day is $60. So, the total reimbursement for food and lodging would be 60x.
The reimbursement for mileage is $0.65 per mile, and David drove 600 miles. So, the reimbursement for mileage would be 0.65 * 600 = 390.
To find the total reimbursement, we can add the reimbursement for food and lodging to the reimbursement for mileage: Total reimbursement = Reimbursement for food and lodging + Reimbursement for mileage Total reimbursement = 60x + 390
Therefore, the equation that determines the number of days x on the trip is: 60x + 390 = Total reimbursement
Part B: To solve the equation, we need to isolate the variable x.
Step 1: Subtract 390 from both sides of the equation to isolate the term 60x: 60x + 390 - 390 = Total reimbursement - 390 60x = Total reimbursement - 390
Step 2: Divide both sides of the equation by 60 to solve for x: (60x)/60 = (Total reimbursement - 390)/60 x = (Total reimbursement - 390)/60
Each step in solving the equation is justified by the algebraic property of equality, which states that we can perform the same operation on both sides of an equation without changing its equality.
Part C: To find the number of days David spent on the trip, we substitute the given reimbursement value into the equation we derived in Part B.
x = (3390 - 390)/60 x = 3000/60 x = 50
Therefore, David spent 50 days on this trip.

Answered by anu958818 | 2024-06-24

To determine the number of days David spent on his trip, we created and solved the equation 60 x + 390 = 3390 . Following algebraic properties, we found that x = 50 , meaning David spent 50 days on the trip. This calculation included the reimbursement for food, lodging, and mileage.
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Answered by anu958818 | 2024-09-30