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.
How do I explain what is happening graphically where the services are charging the same rate? is this answer correct?
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. All points will give a solution, but where the services are charging the same rate, the common points give the common solution. The systems are consistent and the equations are independent.
To explain what is happening graphically, you can plot the two equations on a coordinate plane. The y-axis represents the total cost and the x-axis represents the number of miles traveled.
For the Crespo Transportation Service equation, y = 32 + 8x, you can plot points on the graph by choosing different values for x and then calculating the corresponding values for y. For example, if x = 0, y = 32, so the point (0, 32) represents the initial cost of $32. If x = 1, y = 40, so the point (1, 40) represents the cost of traveling 1 mile. If you continue this process and connect the points, you will get a straight line.
Similarly, for the Siera Transportation Service equation, y = 24 + 10x, you can plot points and connect them to get another straight line.
The point where the lines intersect represents the mileage at which both services are charging the same rate. In this case, we found that the mileage is 4 miles. You can mark this point on the graph and conclude that at 4 miles, both services are charging the same rate.
So, in summary, graphically, the two equations represent two lines on a coordinate plane. The point where these lines intersect represents the mileage at which both services are charging the same rate.