Question

A car gets 22 miles per gallon​ (mpg) in city driving and 35 mpg in highway driving. The car is driven 276 mi on 9 gal of gasoline. How many miles were driven in the city and how many miles were driven on the​ highway?

Answer 1

To solve this problem, set up a system of equations using the given information and solve for the unknowns.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.

Let's assume that x represents the number of miles driven in the city, and y represents the number of miles driven on the highway.

We can set up the following two equations based on the given information:

x + y = 276 (equation 1)

x/22 + y/35 = 9 (equation 2)

To solve this system of equations, we can use substitution. Solve equation 1 for x to get x = 276 - y. Substitute this expression for x into equation 2:

(276 - y)/22 + y/35 = 9

Multiply both sides of the equation by the least common denominator, which is 1540:

70(276 - y) + 44y = 13860

19320 - 70y + 44y = 13860

Combine like terms:

-26y = -5460

Divide by -26:

y = 210

Substitute this value for y back into equation 1 to solve for x:

x + 210 = 276

x = 66

Therefore, 66 miles were driven in the city and 210 miles were driven on the highway.