Question

It is the end of the budgeting period for John Smith, and he has $200 left in his budget for car rental expenses. He plans to spend this budget on a sales trip throughout the country. He will rent a car that costs $40 per day and $0.50 per mile, and he can spend no more than $200.

a. Define variables.

b. Write an inequality.

Answer 1

John Smith can spend up to $200 on his car rental with a daily cost of $40 and a per mile cost of $0.50. We define x as the number of rental days and y as the number of miles driven.

Step-by-step explanation:

To address the problem at hand, we first need to define variables for the car rental scenario involving John Smith. Let x represent the number of days John rents the car, and y represent the number of miles he drives. Given that John has a budget of $200 and the costs are $40 per day and $0.50 per mile, we can establish a budget equation to demonstrate the relationship between days rented, miles driven, and the budget limit.

To write an inequality that represents this scenario:

• Cost per day: $40
• Cost per mile: $0.50
• Total budget: $200

Our inequality will be:

40x + 0.50y ≤ 200

This inequality represents the combination of days (x) and miles (y) that John can afford with his $200 budget, where he cannot exceed this amount.