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)
Responses
10 + 8x > 6 + 10x; x < 2
10 + 8x > 6 + 10x; x < 2
6+10x < 10 + 8x; x > 2
6+10x < 10 + 8x; x > 2
10+ 8x < 6 + 10x; x > 2
10+ 8x < 6 + 10x; x > 2
6 + 10 x > 10 + 8x; x < 2
The correct inequality representing the number of hours where Option A will be the cheaper rental company is:
10 + 8x > 6 + 10x; x < 2
This means that for any number of hours less than 2, the rental from Option A will be cheaper.
To find the number of hours where Option A will be the cheaper rental company, we need to compare the costs of both companies.
For Company A, the cost is a fixed $10 plus $8 per hour, so the cost is given by the expression 10 + 8x, where x represents the number of hours.
For Company B, the cost is a fixed $6 plus $10 per hour, so the cost is given by the expression 6 + 10x, where x represents the number of hours.
To determine when Option A is cheaper, we need to find when the cost of Company A is less than the cost of Company B.
We can write this as an inequality:
10 + 8x < 6 + 10x
To solve this inequality, we can start by simplifying:
8x - 10x < 6 - 10
-2x < -4
To isolate the variable x, we need to divide both sides of the inequality by -2. Since we are dividing by a negative number, we need to flip the inequality sign:
x > 2
Therefore, the inequality representing the number of hours where Option A will be the cheaper rental company is x > 2. This means that for x values greater than 2, Option A will be the cheaper rental company.
The correct inequality representing the number of hours where Option A will be the cheaper rental company is:
10 + 8x > 6 + 10x; x < 2