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.
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