Respuesta :
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.
The maximum number of miles the truck can be driven so that the rental cost is at most [tex]\$1000[/tex] is [tex]\boxed{1423{\text{ miles}}}.[/tex]
Further explanation:
Given:
A local company rents a moving truck for [tex]\$ 750.[/tex]
Rent per mile is [tex]\$ 0.59[/tex] if the truck moves more than 1000 miles.
Explanation:
The rental cost of the truck is [tex]\$ 750[/tex] if he drove less than 1000 miles.
[tex]{\text{Cost}} = \$ 750{\text{ }}x \leqslant 1000[/tex]
The rental cost of the truck can be expressed as follows,
[tex]{\text{Cost}} = 750 + 0.59x{\text{ }}x > 1000[/tex]
The rental cost is at most [tex]\$1000.[/tex]
[tex]750 + 0.59x \leqslant 1000[/tex]
The maximum number of miles can be obtained as follows,
[tex]\begin{aligned}0.59x &\leqslant 1000 - 750\\0.59x &\leqslant 250\\x &\leqslant \frac{{250}}{{0.59}}\\x &\leqslant 423.7\\\end{aligned}[/tex]
The maximum number of miles can be obtained as follows,
[tex]\begin{aligned}{\text{Maximum miles}} &= 1000 + 423\\&= 1423 \\\end{aligned}[/tex]
The maximum number of miles the truck can be driven so that the rental cost is at most [tex]\$1000[/tex] is [tex]\boxed{1423{\text{ miles}}}.[/tex]
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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
