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Chapter 2: Problem 74

For exercises \(65-72\), assign a variable, and write an inequality that represents the constraint. The maximum fuel economy of a car is \(\frac{32 \mathrm{mi}}{1 \mathrm{gal}}\). Find the maximum distance it can travel on a full tank of \(12 \mathrm{gal}\) of gasoline.

Short Answer

Expert verified
The maximum distance is 384 miles.

Step by step solution

01

- Assign a Variable

Let's assign the variable \(d\) to represent the maximum distance the car can travel on a full tank of gasoline.
02

- Write the Inequality for Fuel Economy

The fuel economy can be represented as the inequality: \( \frac{d}{12} \leq 32 \), where \(d\) is the distance and 32 is the maximum fuel economy in miles per gallon.
03

- Solve for d

To find \( d \), multiply both sides of the inequality by 12: \( d \leq 32 \times 12 \). This simplifies to \( d \leq 384 \) miles.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

inequality representation
Fuel economy calculations tell us how far a vehicle can travel using a certain amount of fuel. In our problem, the car鈥檚 fuel economy is given as 32 miles per gallon. To find the maximum distance, it can travel on a full tank of 12 gallons, we can use the formula: \[ d \leq 32 \times 12 \] . Multiplying these values gives a distance of \( d \leq 384 \) \, miles. This calculation is straightforward but often a crucial aspect of operational planning, enabling car owners to understand limitations and plan their trips better.

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