Answer:
$1.25
Step-by-step explanation:
Let
equal the flat rate.
Let
equal the one-time membership processing fee.
Start with a system of equations:
![16.50=8f+p](https://tex.z-dn.net/?f=16.50%3D8f%2Bp)
![14=6f+p](https://tex.z-dn.net/?f=14%3D6f%2Bp)
Use the elimination method and multiply your second equation by
to cancel out the
s:
![-1(14=6f+p)](https://tex.z-dn.net/?f=-1%2814%3D6f%2Bp%29)
Now combine the equations:
![16.50=8f+p](https://tex.z-dn.net/?f=16.50%3D8f%2Bp)
![-14=-6f-p](https://tex.z-dn.net/?f=-14%3D-6f-p)
Subtract:
![2.5=2f](https://tex.z-dn.net/?f=2.5%3D2f)
Divide by the coefficient of
, which is
(I rearranged the equation):
![f=1.25](https://tex.z-dn.net/?f=f%3D1.25)
~
Even though we're not solving for the one-time processing fee, to check our work, we'll need to solve for
, so start with the initial system of equations:
![16.50=8f+p](https://tex.z-dn.net/?f=16.50%3D8f%2Bp)
![14=6f+p](https://tex.z-dn.net/?f=14%3D6f%2Bp)
Use the elimination method and multiply the first equation by
, and the second equation by
:
![3(16.50=8f+p)](https://tex.z-dn.net/?f=3%2816.50%3D8f%2Bp%29)
![-4(14=6f+p)](https://tex.z-dn.net/?f=-4%2814%3D6f%2Bp%29)
Multiply:
![49.50=24f+3p](https://tex.z-dn.net/?f=49.50%3D24f%2B3p)
![-56=-24f-4p](https://tex.z-dn.net/?f=-56%3D-24f-4p)
Subtract:
![-6.5=-p](https://tex.z-dn.net/?f=-6.5%3D-p)
Divide by the coefficient of
, which is
(Rearranged equation):
![p=6.5](https://tex.z-dn.net/?f=p%3D6.5)
~
Check your work:
![16.50=8(1.25)+6.5](https://tex.z-dn.net/?f=16.50%3D8%281.25%29%2B6.5)
![14=6(1.25)+6.5](https://tex.z-dn.net/?f=14%3D6%281.25%29%2B6.5)
Solve:
![16.50=16.50](https://tex.z-dn.net/?f=16.50%3D16.50)
![14=14](https://tex.z-dn.net/?f=14%3D14)
It's correct!