Rachelle and Kayla want to rent a boat while they are at Lake Azul. Floatmore Boats charges $5.00 for insurance and $5.25 an hour. Neversink charges $6.75 an hour. You have to pay the insurance fee to rent at Floatmore and a rental for any part of the hour is charged as a full hour. How long must they rent a boat so that Floatmore is the less expensive choice?
you want to find x hours, such that
5.00 + 5.25x < 6.75x
To determine how long Rachelle and Kayla must rent a boat for Floatmore to be the less expensive choice, we need to compare the costs of renting from Floatmore and Neversink.
Let's assume they plan to rent the boat for a certain number of hours, which we will represent as 'x' hours.
For Floatmore:
Cost of insurance = $5.00
Cost per hour = $5.25
Total cost for Floatmore = Cost of insurance + (Cost per hour * Number of hours)
= $5.00 + ($5.25 * x)
= $5.00 + $5.25x
For Neversink:
Cost per hour = $6.75
Total cost for Neversink = Cost per hour * Number of hours
= $6.75 * x
= $6.75x
Now, we need to find the point where the total cost for Floatmore is less than the total cost for Neversink, so:
$5.00 + $5.25x < $6.75x
Simplifying the equation:
$5.00 < $6.75x - $5.25x
$5.00 < $1.50x
Dividing both sides of the inequality by $1.50:
$5.00 / $1.50 < $1.50x / $1.50
3.33 < x
Since the number of hours must be a whole number, we can round up to the nearest hour. Thus, Rachelle and Kayla must rent the boat for at least 4 hours in order for Floatmore to be the less expensive choice.