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.(1 point)

Answer 1

Let's start by writing an inequality for Company A. Company A charges a fixed amount of $10 plus $8 per hour, so the total cost for Company A can be represented as: $10 + $8x, where x represents the number of hours.

Next, let's write an inequality for Company B. Company B charges a fixed amount of $6 plus $10 per hour, so the total cost for Company B can be represented as: $6 + $10x, where x represents the number of hours.

Now, we want to find the number of hours where Option A will be the cheaper rental company. This means we want to find the x values that make the total cost for Company A less than the total cost for Company B.

Mathematically, this can be represented as:
$10 + $8x < $6 + $10x

To solve this inequality, we can subtract $6 from both sides of the inequality:
$10 + $8x - $6 < $6 + $10x - $6
$4 + $8x < $10x

Next, let's isolate the x term by subtracting $8x from both sides of the inequality:
$4 + $8x - $8x < $10x - $8x
$4 < $2x

Finally, we can divide both sides of the inequality by 2 to solve for x:
$4/2 < $2x/2
2 < x

Therefore, the inequality representing the number of hours where Option A will be the cheaper rental company is x > 2.