kuvyojhmoob one year ago A salesperson purchased an automobile that was advertised as averaging 27 mi/gal in the city and 38 mi/gal on the highway. A recent sales trip that covered 1978 miles required 59 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?

1. anonymous

Assume the number of miles driven in the city is $$x$$. Then the amount of gas used in the city is $$\frac{x}{27}$$. The number of miles driven on the highway is therefore $$1978-x$$ and the amount of gas used on the highway is $$\frac{1978-x}{38}$$. The total amount of gas used is then$\frac{ x }{ 27 } + \frac{ 1978-x }{ 38 } = 59$Solve for $$x$$.

2. kuvyojhmoob

×=648

3. mathmate

Yes, x=648 is correct x/27+1978/38-x/38=59 x/27-x/38=59-1978/38 multiply by 27*38=1026 to eliminate the denominators 38x-27x =60354-1978=7128 x=7128/12=648