Answer:
Mid grade gas per gallon = $2.67
Regular gas per gallon = $2.37
Step-by-step explanation:
Let, x= mid grade gas, y=regular gas.
So, for 18 gallons of mid grade gas and 5 gallon of regular gas at $59.91, it can be expressed as,
------------------(equation 1)
for 14 gallon of mid grade gas and 1 gallon of regular gas at 39.75, it can be expressed as,
-------------------(equation 2)
-------------------(equation 3)
Now substituting the value of y from (equation 3) in (equation 1) we get,
![18x+5y=59.91](https://tex.z-dn.net/?f=18x%2B5y%3D59.91)
![18x+5(39.75-14x)=59.91](https://tex.z-dn.net/?f=18x%2B5%2839.75-14x%29%3D59.91)
![18x+198.75-70x=59.91](https://tex.z-dn.net/?f=18x%2B198.75-70x%3D59.91)
![52x=198.75-59.91](https://tex.z-dn.net/?f=52x%3D198.75-59.91)
![52x=138.84](https://tex.z-dn.net/?f=52x%3D138.84)
![x=\frac{138.84}{52}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B138.84%7D%7B52%7D)
-------------------------(equation 4)
Now substituting value of x from (equation 4) in (equation 3) we get,
![y=39.75-14x](https://tex.z-dn.net/?f=y%3D39.75-14x)
![y=39.75-(14\times2.67)](https://tex.z-dn.net/?f=y%3D39.75-%2814%5Ctimes2.67%29)
![y=39.75-37.38](https://tex.z-dn.net/?f=y%3D39.75-37.38)
![y=2.37](https://tex.z-dn.net/?f=y%3D2.37)
Therefore price per gallon of mid grade gas is x = $2.67, and price per gallon of regular gas y = $2.37.