Question

Tony fills his car with gas. His tank holds 14.0 gallons of gas. He pumps 8.37 gallons into the tank. If his car averages 27.6 miles per gallon, how far could he have driven before running out of gas had he not stopped to fill up? Give your answer to the nearest whole mile. A. 155 miles B. 386 miles C. 462 miles D. 617 miles

Short answer

A. 155 miles

Step-by-step solution

- Understand the Problem

Determine how many gallons of gas Tony had in the tank before he filled it up.

- Calculate Remaining Gallons

Subtract the amount of gas Tony pumped from the total capacity of the tank: 14.0 gallons (total capacity) - 8.37 gallons (pumped) = 5.63 gallons (remaining)

- Determine Miles per Gallon

Given the car averages 27.6 miles per gallon.

- Calculate Total Distance

Multiply the remaining gallons by the miles per gallon to find the total distance Tony could drive: 5.63 gallons * 27.6 miles per gallon = 155.38 miles

- Round to Nearest Whole Mile

Round 155.38 miles to the nearest whole mile, which gives 155 miles.

- Select the Correct Answer

Compare the rounded distance to the given options and choose the closest number: A. 155 miles

Key concepts

arithmetic operations

Arithmetic operations involve basic mathematical procedures such as addition, subtraction, multiplication, and division. These operations are fundamental in solving almost any math problem. In our exercise, the arithmetic operations used are subtraction and multiplication.

First, we subtract the amount of gas Tony pumped into his car (8.37 gallons) from the car's total tank capacity (14.0 gallons). This tells us how much gas was already in the tank before he filled it up:
\[\begin{equation} 14.0 - 8.37 = 5.63 \text{ gallons (remaining)} \to \end{equation}\]
Next, we multiply the remaining gallons by the car's mileage rate (27.6 miles per gallon) to find out how many miles Tony could have driven before refilling:
\[\begin{equation} 5.63 \text{ gallons} \times 27.6 \text{ miles per gallon} = 155.38 \text{ miles (total distance)} \to \end{equation}\]
By practicing these fundamental operations, students can strengthen their problem-solving skills.

distance calculation

In this problem, calculating distance involves knowing how far Tony's car can travel on a certain amount of gas. This is done using the vehicle's mileage rate, which is the distance it can travel per unit of fuel—in this case, miles per gallon.

To find out the total distance Tony could have traveled with the remaining gas, we multiply the remaining gallons by the miles per gallon value:
\[\begin{equation} 5.63 \text{ gallons} \times 27.6 \text{ miles per gallon } = 155.38 \text{ miles} \to \end{equation}\]
Rounding this to the nearest whole mile, we get 155 miles. This means Tony could have driven 155 miles before he had to stop to refill his tank.

Understanding how to calculate distance using different formulas and given data is particularly helpful in many real-world scenarios, like planning trips or estimating fuel consumption.

unit conversion

Unit conversion plays an essential role in solving various mathematical problems, especially those involving measurements and distances. Although in this exercise we didn't explicitly convert units, understanding units is crucial for clarity and accuracy.

In our example, we worked with gallons for fuel and miles for distance. The critical piece of information is the car's fuel efficiency given in miles per gallon (27.6 miles per gallon).
This mileage rate implicitly converts the amount of gas to the distance Tony could travel.

Unit conversions could include changing measures from miles to kilometers, gallons to liters, or similar conversions. Knowing how to handle units ensures calculations are accurate, and answers are meaningful based on the problem's context.

• 1 mile = 1.60934 kilometers
• 1 gallon = 3.78541 liters

Understanding unit conversion and applying it correctly can simplify problems involving various measurements and help ensure that final answers are in the desired units.