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Chapter 5: Problem 8

Lenny's car gets approximately 20 miles per gallon. He is planning a 750 -mile trip. a. About how many gallons of gas should Lenny plan to buy? b. At an average price of \(\$ 4.10\) per gallon, how much should Lenny expect to spend for gas?

Short Answer

Expert verified
a. Lenny should plan to buy approximately 37.5 gallons of gas for his trip. b. Lenny should expect to spend about $153.75 for gas.

Step by step solution

01

Calculate the Required Gallons of Fuel

To calculate the number of gallons of fuel required for the trip, divide the total distance of the trip (750 miles) by the car's fuel efficiency (20 miles per gallon). The equation is \(\frac{750}{20}\).
02

Determine the Fuel Cost

Once the required gallons of fuel is calculated, multiply that figure with the cost of one gallon of fuel ($4.10). So, the equation becomes \(\text{Required Gallons of Fuel} * 4.10\).

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Key Concepts

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

Fuel Consumption Calculation
Understanding fuel consumption is crucial for anyone planning a trip. It's a practical application of math in everyday life. For Lenny, who gets an average of 20 miles per gallon with his car, calculating the fuel needed for a 750-mile trip involves using the concept of division to determine his car's efficiency over that distance.

The formula for calculating the gallons of gas needed is straightforward:
\[\text{Gallons Needed} = \frac{\text{Total Distance}}{\text{Miles per Gallon}}\]
In Lenny鈥檚 case, we divide the total distance of 750 miles by the fuel efficiency rate of 20 miles per gallon. This division gives us the unit rate or how many gallons he will consume per unit of distance traveled. So,
\[\text{Gallons Needed} = \frac{750}{20}\]
After performing the calculation, Lenny will know exactly how many gallons to purchase before heading out on his trip. This calculation is not only helpful for trip planning, but also for budgeting and understanding a vehicle's environmental impact.
Budgeting for Trip Expenses
Once Lenny knows how many gallons of gas he will need, the next step is to calculate his expected expenses for fuel. To forecast his trip's budget accurately, Lenny multiplies the number of gallons by the cost per gallon.

This formula embodies a simple multiplication:
\[\text{Total Fuel Cost} = \text{Gallons Needed} \times \text{Price per Gallon}\]
Let's assume Lenny has calculated that he will require 37.5 gallons of fuel for his 750-mile journey. With the price of gas at $4.10 per gallon, Lenny can expect to spend:
\[\text{Total Fuel Cost} = 37.5 \times 4.10\]
By understanding this aspect of trip planning, one can make informed decisions, such as whether it's cheaper to drive or take alternative transportation. It's a vital life skill for personal finance management and reinforces the importance of math in making cost-effective choices.
Unit Rate Problem
A unit rate problem involves finding the cost per unit of a single item or measure, which is often used in comparing prices or efficiencies. In Lenny's scenario, the 'unit' is one mile of travel in his car. The 'rate' refers to the cost or quantity related to one unit of measure鈥攊n this case, gas needed per mile.

To calculate the unit rate, we use the following formula:
\[\text{Unit Rate} = \frac{\text{Total Quantity}}{\text{Total Units}}\]
For example, in Lenny鈥檚 journey, knowing the fuel consumption rate per mile is useful in planning. The fuel efficiency of Lenny鈥檚 car can be expressed as a unit rate (20 miles per gallon), which means for every gallon of gas, his car can travel 20 miles. This information helps Lenny estimate the amount of fuel he'll need, regardless of the trip distance. Grasping how to solve unit rate problems is fundamental in various everyday applications, from determining the best buy in a supermarket to evaluating the fuel efficiency of vehicles.

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Most popular questions from this chapter

There are 5,280 feet in a mile. Round answers to the nearest unit. a. How many miles does a car traveling at 42 mi/h go in one hour? b. How many feet does a car traveling at 42 mi/h go in one hour? c. How many feet does a car traveling at 42 mi/h go in one minute? d. How many feet does a car traveling at 42 mi/h go in one second? e. How many miles does a car traveling at x mi/h go in one hour? f. How many feet does a car traveling at x mi/h go in one hour? g. How many feet does a car traveling at x mi/h go in one minute? h. How many feet does a car traveling at x mi/h go in one second?

Megan has a friend at work who is selling a used Honda. The car has 60,000 miles on it. Megan comparison shops and finds these prices for the same car. $$\begin{array}{c}{\text { Price }} \\ \hline \$ 22,000 \\ {\$ 19,000} \\\ {\$ 18,000} \\ {\$ 16,700} \\ {\$ 15,900}\end{array}$$ a. Find the mean price of the 5 prices listed. b. How many of these cars are priced below the mean? c. Find the median price. d. How many of these cars are priced below the median?

Megan, from Exercise 8, decides to get more information about the cars she researched. The table has prices and mileages for the same used car. In addition to the statistics she has learned in this chapter, Megan decides to use her linear regression skills from Chapter 2 to see if there is a relationship between the prices and the mileage. She hopes to use this knowledge to negotiate with sellers. $$\begin{array}{|c|c|}\hline{\text { Mileage, } x} & {\text { Price, } y} \\\ \hline 21,000 & {\$ 22,000} \\ {30,000} & {\$ 19,000} \\ {40,000} & {\$ 18,000} \\ {51,000} & {\$ 16,700} \\ {55,000} & {\$ 15,900}\\\ \hline\end{array}$$ a. Enter the data into your calculator. Find the regression equation. Round to the nearest hundredth. b. Find the correlation coefficient r. Round to three decimal places. c. Is the regression equation a good predictor of price, given the mileage? Explain. d. The car Megan is considering has \(60,000\) miles on it and the price is \(\$ 19,000 .\) Discuss her negotiating strategy. Explain on what grounds she should try to get a lower price.

Ghada works for an insurance company as an accident reconstruction expert. She measured a 52-ft chord from the outer rim of the yaw mark on the road surface. The middle ordinate measured x ft in length. The drag factor of the road surface was determined to be 1.05. a. What is the expression for the radius of the yaw mark? b. Determine the expression for the minimum speed that the car was going when the skid occurred.

Seamus bought a car that originally sold for \(\$ 40,000 .\) It exponentially depreciates at a rate of 7.75\(\%\) per year. Write the exponential depreciation equation for this car.
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