Question

A certain homeowner uses a gas edger to clean up his lawn every time he mows. If the edger uses 160 milliliters of fuel each time, what is the maximum number of times the homeowner can edge his lawn with 8 liters of fuel? \((1\) liter \(=1,000\) milliliters \()\) A) 5 B) 50 C) 100 D) 1,000 $$ \begin{aligned} &\text { Assignment Choice for Two Physics Classes }\\\ &\begin{array}{|l|c|c|c|} \hline & \text { Dr. Soper } & \text { Mr. Coelho } & \text { Total } \\ \hline \text { Lab Report Only } & 17 & 21 & 38 \\ \hline \begin{array}{l} \text { Lab Report and Final } \\ \text { Exam } \end{array} & 3 & 2 & 5 \\ \hline \text { Total } & 20 & 23 & 43 \\ \hline \end{array} \end{aligned} $$

Short answer

The homeowner can use the gas edger a maximum of 50 times with 8 liters of fuel. So, the correct answer is \(B\) 50.

Step-by-step solution

Convert liters of fuel to milliliters

Given that 1 liter equals 1,000 milliliters, we need to convert 8 liters of fuel into milliliters using the conversion factor for liters to milliliters. \[8 \text{ liters} \times \frac{1,000 \text{ milliliters}}{1 \text{ liter}}\]

Calculate the total amount of fuel in milliliters

Now, multiply 8 by 1,000 to find the total amount of fuel in milliliters. \[8 \times 1,000 = 8,000 \text{ milliliters}\] So, the homeowner has 8,000 milliliters of fuel available.

Divide the total fuel by the fuel consumed each time

Since the edger consumes 160 milliliters of fuel each time, to find the maximum number of times the homeowner can use the edger, divide the total fuel by the fuel consumed each time. \[\frac{8,000 \text{ milliliters}}{160 \text{ milliliters/use}}\]

Calculate the maximum number of uses

Divide 8,000 by 160 to find the maximum number of times the homeowner can use the edger before the fuel runs out. \[\frac{8,000}{160} = 50\] So, the homeowner can use the gas edger a maximum of 50 times with 8 liters of fuel. The correct answer is B) 50.

Key concepts

Understanding Unit Conversion

Unit conversion is all about changing measurements from one unit to another. It is crucial for comparing different types of measurement that use different units. In the context of the exercise, we need to convert liters to milliliters, because the edger's fuel consumption is measured in milliliters.
To convert:

• Identify the relationship between the two units known from the problem, here, 1 liter = 1,000 milliliters.
• Multiply the amount in liters by the conversion factor to obtain the amount in milliliters.

For instance, multiplying 8 liters by 1,000 gives 8,000 milliliters. This simple multiplication enables us to work with a single unit for all calculations.

Performing Arithmetic Calculations

Arithmetic calculations involve basic mathematical operations such as addition, subtraction, multiplication, and division. In solving conversion problems, these operations are often used.
For the provided exercise:

• We start by multiplying to convert units (8 liters to 8,000 milliliters).
• Then, we need to divide the total amount by the amount used each time to find the number of uses.

Thus, performing \[ \frac{8,000}{160} = 50 \] involves straightforward division.
Such calculations require precision to ensure that each step is correctly handled.

Effective Problem-Solving Steps

Tackling any problem efficiently hinges on clear and logical problem-solving steps. This involves breaking down the problem into manageable parts.
For the exercise at hand:

• Identify the units involved: Notice the units given and what needs conversion.
• Convert the units to work with consistent measurements.
• Calculate by applying arithmetic operations to answer the question.

These steps form a robust approach ensuring a systematic path to the solution. They help avoid errors and provide clarity through the problem-solving process.

Mastering Fuel Consumption Calculation

Fuel consumption calculation is about determining how much fuel is used for specific activities. It can be crucial for understanding efficiency and planning.
In the edger exercise:

• Recognize how much fuel is used each time, i.e., 160 milliliters.
• Calculate how often an activity can be repeated with available resources, in this case dividing total fuel quantity by the consumption per use.

Knowledge of such calculations is not just applicable to physical gadgets but extends to various applications in daily life. For this example, we determined that the maximum number of uses was 50, indicating how resource planning and unit conversions come together. The answer, while calculated using simple operations, offers vital insights into effective consumer behavior.