Question

Gasoline costs \(\$ 3.15\) per gallon. Which equation shows the total cost \(C\) of buying \(g\) gallons of gasoline? A. \(C=\frac{g}{3.15}\) B. \(g=3.15 C\) C. \(g=\frac{3.15}{C}\) D. \(C=3.15 g\)

Short answer

Option D: \[ C = 3.15g \]

Step-by-step solution

- Identify Variables and Constants

Identify the variables and constants in the problem. Here, the total cost is denoted by C, and the number of gallons is denoted by g. The constant is the price per gallon, which is given as $3.15.

- Understand the Relationship

Understand the relationship between the total cost C and the number of gallons g. The total cost is obtained by multiplying the number of gallons by the price per gallon.

- Formulate the Equation

Since the total cost is obtained by multiplying the price per gallon by the number of gallons, the equation is: \[ C = 3.15g \]

- Choose the Correct Option

Compare the formulated equation with the given options. The correct option that matches \[ C = 3.15g \] is option D.

Key concepts

solving equations

When tackling algebra problems, a key skill you need is the ability to solve equations. This involves finding the value of one or more variables that make an equation true. In the context of the given exercise, you have to determine the cost of gasoline based on the number of gallons purchased.

We start by identifying the variables: \( g \) stands for the number of gallons of gasoline, and \( C \) represents the total cost. And don’t forget the constant value, which here is the price per gallon, \( 3.15 \) dollars.

Next, understand the relationship: the total cost (\( C \)) is directly proportional to the number of gallons (\( g \)). That means you multiply the number of gallons by the price per gallon to get the total cost. Hence, the suitable equation becomes \[ C = 3.15g \].

Solving equations often involves:

• Identifying variables and constants.
• Understanding the relationships between them.
• Setting up the correct arithmetic or algebraic expression.

Once you have created an equation, the next task is to solve for the unknown, ensuring all units and values are properly managed throughout the steps.

cost calculation

Calculating costs becomes straightforward when you understand how the variables relate to each other. In problems involving purchases, you typically multiply the quantity of items by their unit price.

In our exercise, the price per gallon (\( 3.15 \) dollars) is multiplied by the number of gallons bought (\( g \)). This kind of multiplication tells us how much we will spend in total. Hence, the calculation goes like this:

If you buy \( 10 \) gallons of gasoline, the **total cost** (\( C \)) will be:

\[ C = 3.15 \times 10 = 31.5 \] dollars.

Key steps in any cost calculation include:

• Identifying all the unit values and quantities.
• Using multiplication to find the total costs.
• Ensuring all units (like dollars, gallons, etc.) are accounted for.

It’s crucial to keep your work organized to avoid mistakes, and always double-check your computations.

unit prices

Understanding unit prices is essential in many real-life scenarios, from grocery shopping to budgeting fuel expenses. A unit price tells you the cost per single unit of an item, which helps compare different products and make informed decisions.

In this exercise, the unit price is \( 3.15 \) dollars per gallon of gasoline. This means for every gallon you purchase, you will pay \( 3.15 \) dollars.

To use unit prices effectively:

• Identify the cost for a single unit (in this case, one gallon).
• Multiply the unit price by the total number of units to find the overall cost (total cost for multiple gallons).
• Compare unit prices across different sellers to find the best deal.

For example, if another station sells gasoline at \( 3.00 \) dollars per gallon, buying from there could save you money.

Always verify unit prices to manage expenses smartly and avoid overpaying.