A bounce house rental company A charges a fixed amount of $30 plus $5 per hour for renting a bounce house. Company B charges a fixed amount of $10 plus $15 per hour for renting a bounce house. Write and solve an inequality representing the number of hours where Option A will be the cheaper rental company. Let x represent the number of hours.
For option A, the cost can be represented as $30 + $5x, where x is the number of hours.
For option B, the cost can be represented as $10 + $15x, where x is the number of hours.
To find the number of hours where option A will be the cheaper rental company, we need to find the values of x for which the cost of option A is less than the cost of option B.
So, we have the equation:
$30 + $5x < $10 + $15x
Now, we can subtract $10 and $5x from both sides of the equation to isolate the variables on one side:
$20 < $10x
Next, we divide both sides of the equation by $10 to solve for x:
2 < x
Therefore, the inequality representing the number of hours where option A will be the cheaper rental company is x > 2.