Question

You decide to rent a scooter to tour downtown Orlando on Monday. The rental company offers you two options. Option A is to pay a $10 fee for the day and $0.50 per mile driven. Option B is to pay a $27.50 fee, but you have unlimited mileage included (so you don't have to pay anything additional for the miles you put on the scooter.) Write an inequality that expresses when Option B would be cheaper. A. Option A is always cheaper. B. B(s) > 35 C. B(s) ≤ 35 D. B(s) = 17.50

Answer 1

Let's write the costs for each option:

Option A: $10 fee for the day, plus $0.50 per mile driven.

Then if you drive x miles, the cost will be:

Ca(x) = $10 + $0.50*x

Option B: this is a fixed $27.50

Cb(x) = $27.50

(notice that cost b does not depend on x)

Now we can find the value of x such that bot costs are equal:

Cb(x) = Ca(x)

$27.50 = $10 + $0.50*x

$27.50 - $10 = $0.50*x

$17.50/$0.50 = x

35 = x

Then if you drive exactly 35 miles, the cost of both options will be the same ($27.50).

Now, if you drive less than 35 miles, the option A wil be cheaper, because the y-intercept is smaller.

If you drive more than 35 miles, option B will be cheaper, because the slope is smaller.

Then the solution is:

Option B is cheaper for more than 35 miles (and the same for exactly 35 miles)

So the correct option is option B, for x > 35 miles, option B is cheaper.

(in the options there is the notation B(s) > 35) i interpret that this means "more than 35 miles"