Answer:
a) [tex]91\,+\,0.14 \,x \leq 140[/tex] where "[tex]x[/tex]" stands for the number of miles driven.
b) He can drive as far as 250 miles to keep the rental cost limited to $140.
Step-by-step explanation:
a) Robert wants to make sure that the addition of the costs coming from the car rental per week ($91) plus the amount paid for the coverage of "x" number of miles (which goes as $0.14 times x) does not exceed $140 (which is the same as saying that this total cost must be smaller than or equal to $140.
In math terms, such is written as:
[tex]91\,+\,0.14 \,x \leq 140[/tex]
where "x" stands for the number of miles driven.
b) the total number of miles (x) he is allowed to cover given the $140 restriction is obtained by solving for "x" (the number of driven miles) in the inequality of part a):
[tex]91\,+\,0.14 \,x \leq 140\\0.14\,x\leq 140-91\\0.14\,x\leq 49\\x\leq \frac{49}{0.14} \\x\leq 350[/tex]
which tells us that the number of driven miles (x) has to be smaller or equal to 350 miles. Then he can drive as far as 250 miles to keep the rental cost limited to $140.
