A salesperson purchased an automobile that

was advertised as averaging 25

mi+gal in the city and

40 mi+gal on the highway. A recent sales trip that covered

1800 miles required 51 gallons of gasoline. Assuming that

the advertised mileage estimates were correct, how many

miles were driven in the city?

Let the number of miles driven in the city be denoted as \( x \). Then, the number of miles driven on the highway is the remainder of the trip, which can be represented as \( 1800 - x \).

Using the information given:

- The car averages **25 miles per gallon** in the city.
- The car averages **40 miles per gallon** on the highway.

The total gasoline consumption for city driving is:

\[
\frac{x}{25} \quad \text{(gallons)}
\]

The total gasoline consumption for highway driving is:

\[
\frac{1800 - x}{40} \quad \text{(gallons)}
\]

Since the total gasoline used for the entire trip was 51 gallons, we can set up the equation:

\[
\frac{x}{25} + \frac{1800 - x}{40} = 51
\]

To solve this, we first find a common denominator for the fractions:

\[
\frac{40x}{1000} + \frac{25(1800 - x)}{1000} = 51
\]

Simplifying:

\[
\frac{40x + 25(1800 - x)}{1000} = 51
\]

Multiply both sides by 1000 to eliminate the denominator:

\[
40x + 25(1800 - x) = 51000
\]

Now, distribute the 25:

\[
40x + 45000 - 25x = 51000
\]

Simplify:

\[
15x + 45000 = 51000
\]

Subtract 45000 from both sides:

\[
15x = 6000
\]

Now, divide both sides by 15:

\[
x = 400
\]

Thus, **400 miles were driven in the city**.

### Would you like a detailed breakdown of any part of the solution?

Here are 5 related questions to expand your understanding:

1. How would the solution change if the city mileage was 30 mi/gal instead of 25 mi/gal?
2. If the highway mileage was 35 mi/gal, how would the number of city miles driven change?
3. How can we model this problem if the total fuel consumption was unknown but the total cost of gasoline was given?
4. How does this type of problem relate to systems of linear equations?
5. What would happen if the total miles traveled increased to 2000 miles but the gas consumption stayed the same?

**Tip:** Always check your units when solving real-world problems to ensure your equations make sense!

A salesperson purchased an automobile that was advertised as averaging 25 mi/gal in the city and 40 mi/gal on the highway. A recent sales trip that covered 1800 miles required 51 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?

Learn how to calculate the miles driven in the city using a linear equation based on fuel efficiency and total gasoline consumption. This problem explores algebraic concepts and rational expressions suitable for students in Grades 9-12.

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