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)
To determine when Option A will be cheaper, we need to compare the total cost of renting a one-person kayak from both companies.
Let's start by calculating the cost for each company.
For Company A, the cost is fixed at $10 plus $8 per hour, so the total cost can be represented as:
Cost_A = $10 + $8x
For Company B, the cost is fixed at $6 plus $10 per hour, so the total cost can be represented as:
Cost_B = $6 + $10x
To find when Option A will be cheaper, we need to compare the two costs:
Cost_A < Cost_B
Substituting the respective equations for Cost_A and Cost_B, we get:
$10 + $8x < $6 + $10x
Now, let's solve the inequality for x.
$10 - $6 < $10x - $8x
$4 < $2x
Dividing both sides of the inequality by 2:
$2 < x
Therefore, the inequality representing the number of hours where Option A will be the cheaper rental company is x > 2.
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.
To write an inequality representing the number of hours where Option A will be the cheaper rental company, we need to calculate the total cost for each company based on the number of hours of rental.
For Company A, the total cost (C) can be represented as:
C = 10 + 8x
(where x is the number of hours)
For Company B, the total cost (C) can be represented as:
C = 6 + 10x
(where x is the number of hours)
To find the number of hours where Option A will be cheaper, we need to determine when Company A's total cost is less than Company B's total cost. So we need to solve the inequality:
10 + 8x < 6 + 10x
Now, let's solve this inequality step by step:
Step 1: Subtract 6 from both sides:
10 + 8x - 6 < 6 + 10x - 6
4 + 8x < 10x
Step 2: Subtract 8x from both sides:
4 + 8x - 8x < 10x - 8x
4 < 2x
Step 3: Divide both sides by 2:
4 / 2 < 2x / 2
2 < x
So the inequality representing the number of hours where Option A will be cheaper is x > 2. This means that if the number of hours of rental is greater than 2, Option A will be the cheaper rental company.