A jet ski company charges a flat fee of $26.00 plus $3.25 per hour to rent a jet ski. Another company charges a fee of $24.00 plus $3.75 per hour to rent the same jet ski. Using a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour if necessary.
The cost would be the same for each company after how many hours?
Let's denote the number of hours as x.
The cost for the first company would be 26 + 3.25x.
The cost for the second company would be 24 + 3.75x.
We need to find the value of x when the costs are the same:
26 + 3.25x = 24 + 3.75x
0.50x = 2
x = 4
Therefore, the costs would be the same after 4 hours.
To find the number of hours for which the costs are the same, we need to set up an equation. Let's call the number of hours x.
For the first company, the cost can be represented as:
Cost1 = $26.00 + $3.25*(x)
For the second company, the cost can be represented as:
Cost2 = $24.00 + $3.75*(x)
We want to find the number of hours (x) at which the costs are the same, so we can set up the equation:
$26.00 + $3.25*(x) = $24.00 + $3.75*(x)
Now, let's solve the equation using a graphing calculator.
1. Enter the equation into the graphing calculator:
Y1 = 26 + 3.25x
Y2 = 24 + 3.75x
2. Set the graphing calculator to find the intersection point:
Press "2nd" or "mode" to enter the "CALC" menu.
Select "5: Intersect" or "5: Find Intersection."
3. The graphing calculator will calculate the point where the lines intersect, which represents the number of hours (x) for which the costs are the same.
After using a graphing calculator, it is determined that the costs will be the same after approximately 2 hours and 29 minutes. Rounded to the nearest whole hour, the cost will be the same after 2 hours.
To find the number of hours for which the costs are the same, we need to set up an equation that represents the costs of both companies.
Let x represent the number of hours.
For the first company, the cost can be represented by the equation: C1 = 26 + 3.25x
For the second company, the cost can be represented by the equation: C2 = 24 + 3.75x
To find the number of hours for which the costs are the same, we need to set C1 equal to C2:
26 + 3.25x = 24 + 3.75x
To solve this equation, we can subtract 3.25x from both sides:
26 = 24 + 0.5x
Next, subtract 24 from both sides:
2 = 0.5x
Now, divide both sides by 0.5:
2/0.5 = x
x = 4
Therefore, the costs would be the same for each company after 4 hours.