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APPLICATION Portia drove her new car 308 miles on \(10.8\) gallons of gasoline. a. What is the car's rate of gasoline consumption in miles per gallon? b. If this is the typical mileage for Portia's car, how much gas will it take for a 750 -mile vacation trip? c. If gas costs \(\$ 2.35\) per gallon, how much will Portia spend on gas on her vacation? d. The manufacturer advertised that the car would get 30 to 35 miles per gallon. How does Portia's mileage compare to the advertised estimates?

Short Answer

Expert verified
a) 28.52 mpg; b) 26.29 gallons; c) $61.78; d) Below advertised range.

Step by step solution

01

Calculate Mileage in Miles per Gallon

To find the car's rate of gasoline consumption in miles per gallon, divide the total miles driven by the gallons of gasoline used: \[\text{Miles per Gallon} = \frac{\text{Total Miles Driven}}{\text{Gallons Used}} = \frac{308 \text{ miles}}{10.8 \text{ gallons}} \approx 28.52 \text{ miles per gallon}\]
02

Calculate Gas Needed for 750-Mile Trip

Using the car's mileage rate, determine how many gallons of gas will be needed for a 750-mile trip: \[\text{Gallons Needed} = \frac{750 \text{ miles}}{28.52 \text{ miles per gallon}} \approx 26.29 \text{ gallons}\]
03

Calculate Gas Cost for Vacation

To find out how much Portia will spend on gas, multiply the amount of gas needed by the cost per gallon: \[\text{Cost of Gas} = 26.29 \text{ gallons} \times 2.35 \text{ dollars per gallon} \approx 61.78 \text{ dollars}\]
04

Compare Mileage Against Advertised Estimates

Portia's calculated mileage is \(28.52\) miles per gallon. The advertised estimate was between 30 and 35 miles per gallon. Portia's actual mileage is below the advertised range.

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Key Concepts

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

Gasoline Consumption
Gasoline consumption refers to the amount of gasoline used by a vehicle over a certain distance. It's an important factor when considering the efficiency of a car and can be measured in miles per gallon (MPG). In Portia's case, understanding gasoline consumption helped her determine how efficiently her new car used fuel. By driving 308 miles using 10.8 gallons of gas, Portia was able to calculate her car's gasoline consumption rate. To find this rate, she divided the miles driven by the gallons used, resulting in approximately 28.52 miles per gallon (MPG).

Understanding gasoline consumption not only allows drivers to gauge the efficiency of their vehicles, but it also plays a significant role in planning trips and budgeting for fuel costs. Awareness of how much gas is consumed can help set realistic expectations for vehicle performance too. In real-world scenarios, variations in driving habits and conditions might impact gasoline consumption, causing discrepancies between calculated and expected values.
Rate of Consumption
The rate of consumption is a crucial metric that provides insight into how effectively a vehicle uses fuel. Measured in miles per gallon (MPG), it gives a direct indication of how far a vehicle can travel on a single gallon of gasoline. For Portia, determining her car's rate of consumption was an essential first step in planning her upcoming trip. She found that her car's rate was approximately 28.52 MPG by dividing the total miles driven by the gallons consumed.

Having a clear understanding of the rate of consumption helps in predicting fuel needs for longer journeys. For example, to calculate how much fuel Portia would need for a planned 750-mile trip, she divided the trip distance by her car's rate of consumption. This calculation is simple but necessary for effective travel planning.
  • Know your car's efficiency.
  • Plan fuel stops and budget expenses.
Ultimately, understanding the rate of consumption not only ensures a smooth trip but also better managing financial resources when traveling.
Real-World Problem Solving
Real-world problem solving involves applying mathematical concepts to practical situations to find solutions relevant to everyday life. In the context of Portia's car usage and travel plans, she utilized basic math skills to evaluate her vehicle's performance, plan for future journeys, and budget her expenses effectively.

Portia was faced with multiple questions that required logical steps to resolve. First, calculating her car's fuel efficiency allowed her to assess actual performance compared to advertised estimates. Next, understanding fuel consumption rates enabled her to plan for a long-distance trip, providing clarity on fuel requirements and costs. Finally, estimating the total cost of gasoline based on current prices allowed for effective financial preparation.
  • Identify the problem.
  • Break it down into smaller steps.
  • Calculate and compare results for informed decisions.
These processes demonstrate how math skills can transition from theory to real-world application, offering practical solutions for day-to-day challenges and informed decision-making.

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Most popular questions from this chapter

APPLICATION Recipes in many international cookbooks use metric measurements. One cookie recipe calls for 120 milliliters of sugar. How much is this in our customary unit "cups"? (There are 1000 milliliters in a liter, \(1.06\) quarts in a liter, and 4 cups in a quart.)

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