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 $3.50 per hour to rent the same jet ski.%0D%0A%0D%0AUsing a graphing calculator, find the number of hours for which the costs are the same. Round your answer to the nearest whole hour.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A2%0D%0A2%0D%0A%0D%0A8%0D%0A8%0D%0A%0D%0A10%0D%0A10%0D%0A%0D%0A12
To find the number of hours for which the costs are the same, we can set up an equation and solve for the number of hours.
Let's represent the number of hours as "x".
For the first company, the cost is given by C1 = 26 + 3.25x.
For the second company, the cost is given by C2 = 24 + 3.50x.
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 + 3.50x
Simplifying the equation, we have:
2 = 0.25x
Dividing both sides by 0.25, we get:
x = 8
Therefore, the costs are the same after 8 hours.
To find the number of hours for which the costs are the same between the two companies, we need to set up an equation.
Let's denote the number of hours as "x".
For the first company, the cost is given by the equation:
Cost1 = $26.00 + $3.25x
For the second company, the cost is given by the equation:
Cost2 = $24.00 + $3.50x
To find the number of hours where the costs are equal, we need to solve the equation:
Cost1 = Cost2
So, we set up the equation:
$26.00 + $3.25x = $24.00 + $3.50x
Now, we can use a graphing calculator to solve this equation and find the value of "x" at which the costs are equal.
1. Enter the equation into the graphing calculator: Y1 = 26 + 3.25x and Y2 = 24 + 3.50x.
2. Plot the graphs of the two equations on the graphing calculator.
3. Find the point where the two graphs intersect. This will indicate the number of hours at which the costs are the same.
4. Read the x-coordinate of the intersection point, rounded to the nearest whole number.
Based on the provided possible values, it seems that the correct answer is 8 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.
Let's assume the number of hours is represented by x.
For the first company, the cost can be calculated using the equation: Cost = 26 + 3.25x.
For the second company, the cost can be calculated using the equation: Cost = 24 + 3.50x.
Setting these two equations equal to each other, we get:
26 + 3.25x = 24 + 3.50x.
Now, let's solve this equation step-by-step:
1. Move all terms containing x to one side of the equation:
3.25x - 3.50x = 24 - 26.
2. Simplify:
-0.25x = -2.
3. Divide both sides of the equation by -0.25 to isolate x:
x = -2 / -0.25.
4. Simplify:
x = 8.
Therefore, the costs are the same after 8 hours.