The Mitchell family is renting a boat for the day. The boat rental has a flat fee of $100 plus $20 for each hour. They have to pay for a whole hour even if they are not out on the lake for a whole hour. For example, if they rent the boat for 3 and one-half hours, they have to pay for 4 hours.
If they want to spend $250 or less on the boat rental for the day, how many hours can they rent the boat? Formulate an inequality and solve.
Let's call the number of hours they rent the boat "h". The total cost of renting the boat for "h" hours can be expressed as:
Total cost = flat fee + (hourly rate x number of hours)
Total cost = $100 + ($20 x h)
To find the maximum number of hours they can rent the boat for $250 or less, we need to set up an inequality. We know that the total cost must be less than or equal to $250:
$100 + ($20 x h) ≤ $250
Now we can solve for "h" by isolating it on one side of the inequality:
$20 x h ≤ $150
h ≤ $150 ÷ $20
h ≤ 7.5
We can't rent the boat for a fraction of an hour, so we should round down to the nearest whole number. Therefore, the Mitchell family can rent the boat for a maximum of 7 hours if they want to spend $250 or less.