A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car. Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
9
3
5
8
Let x be the number of days for which the costs are the same.
For agency 1, the cost is 110 + 46x.
For agency 2, the cost is 70 + 54x.
Setting the two costs equal to each other, we get 110 + 46x = 70 + 54x.
Subtracting 46x and 70 from both sides, we get 40 = 8x.
Dividing both sides by 8, we get x = 5.
The costs are the same for 5 days.
Therefore, the answer is 5.
To find the number of days for which the costs are the same, we need to set up and solve an equation using the given information.
Let's assume the number of days is represented by "x".
For the first rental car agency, the total cost can be calculated using the equation:
Cost1 = $110.00 + $46.00 * x
For the second rental car agency, the total cost can be calculated using the equation:
Cost2 = $70.00 + $54.00 * x
We want to find the value of "x" when Cost1 = Cost2.
Setting up the equation:
$110.00 + $46.00 * x = $70.00 + $54.00 * x
Now we can solve this equation.
$110.00 - $70.00 = ($54.00 - $46.00) * x
$40.00 = $8.00 * x
To isolate "x", we divide both sides of the equation by $8.00:
40/8 = x
5 = x
Therefore, the costs of the two rental car agencies will be the same after 5 days.
To find the number of days for which the costs are the same for both rental car agencies, we need to set up an equation where the total cost of renting the car from the first agency is equal to the total cost of renting the car from the second agency. Let's denote the number of days as "x".
For the first agency, the total cost can be calculated using the equation:
Cost_1 = 110 + 46x
For the second agency, the total cost can be calculated using the equation:
Cost_2 = 70 + 54x
Setting the two costs equal to each other, we have:
110 + 46x = 70 + 54x
Now let's solve for "x" using a graphing calculator.
Step 1: Enter the equation into the graphing calculator:
110 + 46x = 70 + 54x
Step 2: Graph the line for each side of the equation.
Step 3: Find the point of intersection on the graph which represents the number of days for which the costs are the same.
After following these steps, the graphing calculator will give us the value of "x" at the point where the two lines intersect. This is the number of days for which the costs are the same.
Let's perform the calculation using a graphing calculator.