Question

The cost of a car rental is $40 per day plus 22¢ per mile. You are on a daily budget of $84. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Put answer as an inequality

Answer 1

($0.22/mile)x + $40/day ≤ $84/day, where x is the miles/day

Explanation:

Let y be the cost for a day of car rental, including the mileage fee of $0.22/mile. Let x be the number of miles driven each day.

y = ($0.22/mile)x + $40

The total cost for 100 miles in one day would be = ($0.22/mile)(100 miles) + $40, or $62.

But we are restricted to a daily budget of $84/day. Since we need to spend $84/day or less, we can write an inequality:

($0.22/mile)x + $40/day ≤ $84/day

Let's solve for x for the case that y = $84, the upper limit of expense:

($0.22/mile)x + $40 = $84

x = ($84/day-$40/day)/($0.22/mile)

x = 200 miles

We may travel up to 200 miles/day to stay with the $84/day budget.