At a campground, kayak rental company A charges a fixed amount of $10 plus $8 per hour for renting a one-person kayak. Company B charges a fixed amount of $6 plus $10 per hour for a one-person kayak. 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.

Answer 1

For company A, the total cost for renting a kayak for x hours is given by:
Cost for Company A = $10 + $8x

For company B, the total cost for renting a kayak for x hours is given by:
Cost for Company B = $6 + $10x

If Option A is the cheaper rental company, then the cost for Company A must be less than the cost for Company B. Therefore, we can write the following inequality:
$10 + $8x < $6 + $10x

To solve for x, we can start by subtracting $6 from both sides of the inequality:
$4 + $8x < $10x

Then, subtract $8x from both sides of the inequality:
$4 < $2x

Finally, divide both sides of the inequality by $2:
2 < x

So the inequality representing the number of hours where Option A will be the cheaper rental company is:
x > 2