Okay, I think I have arrived at all the answer to the questions thrown my way. However, how do I explain what is happening “graphically”, where the services are charging same rate?
: Your company must use a transportation service to shuttle their corporate partners from the airport for a quarterly meeting. Crespo Transportation Service charges $32 initially plus $8 per mile for every mile traveled. Siera Transportation Service charges $24 initially plus $10 per mile for every mile traveled.
Write an equation in two variables (x & y) that illustrates the costs for the Crespo Transportation Service.
y=32+8x
Write an equation in two variables (x & y) that illustrates the costs for the Siera Transportation Service.
y=24+10x
If the trip is 3 miles, how much does each one charge? If the trip is 6 miles, how much does each one charge? Explain
If the trip is 3 miles then Crespo transportation services would charge $56
y=32+8x
y=32+8(3)
y=32+24
y=56
For Siera transportation service if the trip is 3 miles then the total charge would be $54
y=24+10x
y=24+10(3)
y=24+30
y=54
If the trip is 6 miles then Crespo transportation would charge $80.00
y=32+8(6)
y=32+48
y=80
If the trip was 6 miles then siera transportation would charge 84
y=24+10(6)
y=24+60
y=84
l) At what mileage are both services charging the same rate? Explain.
For the last part:
set the two y values equal
24 + 10x = 32 + 8x
2x = 8
x = 4
Explanation:
I will solve for x by subtracting
8x from each side and by
subtracting 24 from each side to arrive at the solution.
8x+32=10x+24
8x-8x+32=10x-8x+24
32=2x+24
32-24=2x+24-24
8=2x
x=4
Check if x = 4
Checking the first equation:
y = 32 + 8(4) = 64
Checking the second equation:
y = 24 + 10(4) = 64
Both solutions check.
Therefore, the mileage that both are charging the same rate is 4 miles.
Graphically, where the services are charging the same rate, the graphs will intersect. A solution of a system of equations in two variables is an ordered pair that makes both equations true.
To explain what is happening graphically when the services are charging the same rate, we can plot the equations on a graph and see where they intersect.
For the Crespo Transportation Service, the equation is y = 32 + 8x, where y represents the total cost and x represents the number of miles traveled.
For the Siera Transportation Service, the equation is y = 24 + 10x.
To graph these equations, we assign the x-axis to represent the number of miles traveled and the y-axis to represent the total cost.
We plot the points by substituting different values for x in each equation and calculating the corresponding y values.
For example, for the Crespo Transportation Service, when x = 0, y = 32. This gives us the point (0, 32). When x = 1, y = 40. This gives us the point (1, 40).
Similarly, for the Siera Transportation Service, when x = 0, y = 24. This gives us the point (0, 24). When x = 1, y = 34. This gives us the point (1, 34).
We can continue to plot more points for each equation and connect them with a line.
However, in this case, we can see that the point of intersection is x = 4, y = 64. This means that at 4 miles traveled, both services will charge the same rate of $64.
To visualize this on the graph, we plot the point (4, 64) and draw lines connecting this point to the points from each equation. The point of intersection represents the mileage where both services charge the same rate.
Overall, the graph helps us visually understand and explain the point at which both services charge the same rate.