Question

learn and apply
follow the steps below and answer the questions.
a car rental agency charges $10 to reserve a car and $25 per day. you have $160 to spend on the rental car.
what is the maximum number of days you can rent a car?

• an unlimited number of days
• five days
• seven days
• six days

let’s try to come up with an inequality by first trying a simpler case, given the
days, d, of renting. suppose the car is rented for three days.
with the charge of $10 and paying $25 for every day, what was the charge, c?
select
a. $35
b. $75
c. $55
d. $85

Explanation:

Step1: Set up the inequality

The cost \(c\) for renting a car is \(c = 10+25d\), where \(d\) is the number of days. We know that \(c\leq160\). So, \(10 + 25d\leq160\).

Step2: Solve the inequality for \(d\)

Subtract \(10\) from both sides: \(25d\leq160 - 10\), which simplifies to \(25d\leq150\).
Divide both sides by \(25\): \(d\leq\frac{150}{25}\), so \(d\leq6\).

Answer:

A. \(\$35\) (This part seems to be a mis - match. The main answer for the number of days is \(6\) days. But if we consider the second question "with the charge of \(\$10\) and paying \(\$25\) for every day, what was the charge, \(c\) for \(d = 3\) days", then \(c=10+25\times3=10 + 75=\$85\). But based on the first problem (rental days) the answer is \(6\) days. There is some confusion in the problem layout. Assuming the first problem (rental days) is the main one, the answer for days is \(6\) days. If we consider the second calculation (charge for \(3\) days) the charge \(c = 85\) which is option D)