Question

Write an equation of variation to represent the situation and solve for the indicated information The number of gallons g of fuel used on a trip varies directly with the number of miles mtraveled. If a trip of 270 miles required 12 gallons of fuel, how many gallons are requiredfor a trip of 400 miles?

Answer 1

the relation between the miles and gallons is proportional

so

`\begin{gathered} m\propto g \\ m=k* g \\ k=(m)/(g) \end{gathered}`

put m = 270 miles

g = 12 gallons

`k=(270)/(12)`

for m = 400

`\begin{gathered} 400=k* g \\ 400=(270)/(12)* g \\ \end{gathered}`
`\begin{gathered} g=(400*12)/(270) \\ g=17.77\text{ gallons of fuel} \end{gathered}`

so the answer is 17.8 gallons of fuel required for 400 miles