Question

A local company rents a moving truck for $750 plus $0.59 per mile driven over 1000 mi. What is the maximum number of miles the truck can be driven so that the rental cost is at most $1000? (round to the nearest mile.)

Answer 1

Answer: 1750 miles

Step-by-step explanation:

Let x represent the number of miles driven over 1000 miles. The cost of the truck rental is C= 750. For the cost to be at most $1200, solve the inequality: 750 + 0.06x≤1200 Subtract 750 from each side: Divide each side by : 0.06. X≤750

Because x represents the miles over 1000 miles, the renter can drive the truck no more than 1000 + 750 = 1750 miles for the rental cost to be less than or equal to $1200.

Answer 2

The maximum number of miles the truck can be driven so that the rental cost is at most $\ 1000$ is $\boxed{1423{\text{ miles}}}.$

Further explanation:

Given:

A local company rents a moving truck for $\ 750.$

Rent per mile is $\ 0.59$ if the truck moves more than 1000 miles.

Explanation:

The rental cost of the truck is $\ 750$ if he drove less than 1000 miles.

${\text{Cost}} = \ 750{\text{ }}x \leqslant 1000$

The rental cost of the truck can be expressed as follows,

${\text{Cost}} = 750 + 0.59x{\text{ }}x > 1000$

The rental cost is at most $\ 1000.$

$750 + 0.59x \leqslant 1000$

The maximum number of miles can be obtained as follows,

$\begin{aligned}0.59x &\leqslant 1000 - 750\\0.59x &\leqslant 250\\x &\leqslant \frac{{250}}{{0.59}}\\x &\leqslant 423.7\\\end{aligned}$

The maximum number of miles can be obtained as follows,

$\begin{aligned}{\text{Maximum miles}} &= 1000 + 423\\&= 1423 \\\end{aligned}$

The maximum number of miles the truck can be driven so that the rental cost is at most $\ 1000$ is $\boxed{1423{\text{ miles}}}.$

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear inequality

Keywords: local company, rents, moving, truck, $750, $0.59, maximum, 1000 miles, $1000, at most, at least, number of miles, rental cost, driven over