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)
For Company A, the total cost, C, of renting a one-person kayak can be represented by the equation:
C = 10 + 8x
For Company B, the total cost, C, of renting a one-person kayak can be represented by the equation:
C = 6 + 10x
To find the number of hours where Option A will be the cheaper rental company, we need to find the range of values for x where the cost for Company A is less than the cost for Company B.
Let's solve the inequality:
10 + 8x < 6 + 10x
Subtract 6 from both sides:
4 + 8x < 10x
Subtract 8x from both sides:
4 < 2x
Divide both sides by 2:
2 < x
So the inequality representing the number of hours where Option A will be the cheaper rental company is: x > 2
To determine when Option A will be the cheaper rental company, we need to compare the total cost of renting a one-person kayak from both companies.
For Company A:
Total cost = Fixed amount + Hourly rate * Number of hours
Total cost = $10 + $8x
For Company B:
Total cost = Fixed amount + Hourly rate * Number of hours
Total cost = $6 + $10x
We want to find the number of hours where Option A will be cheaper than Option B, so we can set up the inequality:
Total cost from Company A < Total cost from Company B
$10 + $8x < $6 + $10x
Simplifying the inequality, we get:
$8x - $10x < $6 - $10
-$2x < -$4
Dividing both sides of the inequality by -2 (Note: Dividing by a negative number flips the inequality sign), we get:
x > 2
Therefore, the inequality representing the number of hours where Option A will be cheaper than Option B is x > 2.
To solve this problem, we need to compare the costs of renting a one-person kayak from both companies A and B.
Company A charges a fixed amount of $10 plus $8 per hour. So, the total cost for renting a kayak from company A for x hours is given by:
Cost from company A = $10 + $8x
Company B charges a fixed amount of $6 plus $10 per hour. So, the total cost for renting a kayak from company B for x hours is given by:
Cost from company B = $6 + $10x
Since we want to find the number of hours where Option A (company A) will be cheaper than Option B (company B), we can set up the inequality:
Cost from company A < Cost from company B
$10 + $8x < $6 + $10x
Now, let's solve this inequality:
Subtract $6 from both sides:
$10 - $6 + $8x < $6 - $6 + $10x
Simplifying:
$4 + $8x < $10x
Subtract $8x from both sides:
$4 < $10x - $8x
Simplifying:
$4 < $2x
Divide both sides by $2:
$2 < x
Therefore, the inequality representing the number of hours where Option A will be the cheaper rental company is x > 2.