Tom put 18 gallons of mid grade gas in his truck and filled up his empty five gallon gas tank with regular gas for his lawn mower at home. He spent $59.91. The following week, he put 14 gallons of mid grade gas in his truck and topped off his five gallon tank with just one gallon of regular gas. If he paid $39.75 and the prices remained the same, find the price per gallon of mid grade and regular gas

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jitushashi56 jitushashi56 · Answer 1 · 2020-01-01T10:41:49+01:00

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,

[tex]18x+5y=59.91[/tex] ------------------(equation 1)

for 14 gallon of mid grade gas and 1 gallon of regular gas at 39.75, it can be expressed as,

[tex]14x+y=39.75[/tex] -------------------(equation 2)

[tex]y=39.75-14x[/tex] -------------------(equation 3)

Now substituting the value of y from (equation 3) in (equation 1) we get,

[tex]18x+5y=59.91[/tex]

[tex]18x+5(39.75-14x)=59.91[/tex]

[tex]18x+198.75-70x=59.91[/tex]

[tex]52x=198.75-59.91[/tex]

[tex]52x=138.84[/tex]

[tex]x=\frac{138.84}{52}[/tex]

[tex]x=2.67[/tex] -------------------------(equation 4)

Now substituting value of x from (equation 4) in (equation 3) we get,

[tex]y=39.75-14x[/tex]

[tex]y=39.75-(14\times2.67)[/tex]

[tex]y=39.75-37.38[/tex]

[tex]y=2.37[/tex]

Therefore price per gallon of mid grade gas is x = $2.67, and price per gallon of regular gas y = $2.37.