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.(1 point) The cost would be the same for each company after hours.
To find the number of hours for which the costs are the same, we can set up an equation.
Let x be the number of hours.
For the first company, the cost is equal to $26.00 plus $3.25 per hour, which can be represented as 26 + 3.25x.
For the second company, the cost is equal to $24.00 plus $3.75 per hour, which can be represented as 24 + 3.75x.
Setting them equal to each other, we get:
26 + 3.25x = 24 + 3.75x
Subtracting 24 from both sides, we get:
2 + 3.25x = 3.75x
Subtracting 3.25x from both sides, we get:
2 = 0.5x
Dividing both sides by 0.5, we get:
4 = x
So 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 and solve for the variable representing the number of hours.
Letting x represent the number of hours, the cost C1 for the first company is given by the equation:
C1 = 26 + 3.25x
And the cost C2 for the second company is given by the equation:
C2 = 24 + 3.75x
To find the number of hours for which the costs are the same, we set C1 equal to C2 and solve for x:
26 + 3.25x = 24 + 3.75x
Subtracting 3.25x from both sides:
26 = 24 + 0.5x
Subtracting 24 from both sides:
2 = 0.5x
Dividing both sides by 0.5:
x = 4
Therefore, the costs would be the same for each company after approximately 4 hours.
To find the number of hours for which the costs are the same, we need to set up an equation and solve for the variable representing the number of hours.
Let x be the number of hours for which the costs are the same.
For the first company, the cost is given by the equation:
Cost1 = $26.00 + $3.25(x)
For the second company, the cost is given by the equation:
Cost2 = $24.00 + $3.75(x)
To determine when the costs are the same, we can set up an equation by equating the two cost functions:
$26.00 + $3.25(x) = $24.00 + $3.75(x)
Next, we will calculate the value of x using a graphing calculator:
1. Open a graphing calculator.
2. Enter the equation: y1 = 26 + 3.25x
3. Enter the equation: y2 = 24 + 3.75x
4. Graph the two equations.
5. Find the point of intersection of the two graphs.
The x-coordinate of the point of intersection represents the number of hours for which the costs are the same. Round the answer to the nearest whole hour if necessary.
Note: If you don't have access to a graphing calculator, you can solve the equation algebraically:
26 + 3.25x = 24 + 3.75x
0.50x = 2
x = 4
Therefore, the number of hours for which the costs are the same is approximately 4 hours.