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

$\begin{gathered} m\propto g \\ m=k\times g \\ k=\frac{m}{g} \end{gathered}$

put m = 270 miles

g = 12 gallons

$k=\frac{270}{12}$

for m = 400

$\begin{gathered} 400=k\times g \\ 400=\frac{270}{12}\times g \\ \end{gathered}$$\begin{gathered} g=\frac{400\times12}{270} \\ g=17.77\text{ gallons of fuel} \end{gathered}$

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