The distance traveled by a certain vehicle varies directly to the amount of fuel the vehicle consumes. The vehicle traveled 90 mile on 5 gallons of fuel. At the same rate, how far would the vehicle travel on 7 gallons of fuel

Answer:The vehicle covers 126 miles on 7 gallons of fuel.Step-by-step explanation:Given:The distance traveled is directly proportional to the amount of fuel.For [tex]F[/tex] gallons of fuel distance traveled [tex]D[/tex] miles can be given as:[tex]D[/tex] ∝ [tex]F[/tex][tex]D=kF[/tex]where [tex]k[/tex] is constant of proportionality.The vehicle covers [tex]D=90[/tex] miles on [tex]F=5[/tex] gallons.So[tex]90=k(5)[/tex]Dividing both sides by 5.[tex]\frac{90}{5}=\frac{k(5)}{5}[/tex][tex]18=k[/tex]∴ [tex]k=18[/tex]When [tex]F=7[/tex] gallons[tex]D=(18)(7)[/tex][tex]D=126[/tex] miles∴ The vehicle covers 126 miles on 7 gallons of fuel.