Solving For Gas Price An Equation Breakdown

Hey there, math enthusiasts! Today, we're diving into a real-world problem involving gas prices and figuring out the equation that helps us solve it. We've got a scenario where Evelyn filled up her tank, and we want to break down the cost per gallon. Let's get started!

The Gas-Buying Scenario

So, here's the deal: Evelyn bought a total of 8.4 gallons of gas, and it cost her $23.94. The question we're tackling is: Which equation can we use to figure out the price of each individual gallon of gas? Sounds like a job for some algebraic problem-solving, right? We've got four potential equations lined up, and we need to pick the one that makes the most sense. Let's look at the options:

A) $x / 23.94 = 8.4$ B) $23.94x = 8.4$ C) $8.4x = 23.94$ D) $x / 8.4 = 23.94$

Before we jump into the correct answer, let's think about what each part of the problem represents. We know the total gallons, the total cost, and we're trying to find the price per gallon. This is a classic scenario where understanding the relationship between these values is key.

Breaking Down the Equations

Let's analyze each of these equations to see which one fits our situation best. Remember, we're looking for the equation that accurately represents how the price per gallon relates to the total cost and total gallons purchased.

Option A: $x / 23.94 = 8.4$

This equation suggests that if we take the unknown price per gallon (x) and divide it by the total cost ($23.94), we'll get the total gallons (8.4). Does this make logical sense? Not really. Dividing the price per gallon by the total cost doesn't give us any meaningful value related to the gallons purchased. So, this one seems unlikely.

Option B: $23.94x = 8.4$

In this equation, we're multiplying the total cost ($23.94) by the unknown price per gallon (x) and setting it equal to the total gallons (8.4). Again, this doesn't quite align with what we're trying to find. Multiplying the total cost by the price per gallon doesn't logically lead us to the total number of gallons. This equation is a bit of a head-scratcher in this context.

Option C: $8.4x = 23.94$

Now, this equation looks promising. Here, we're multiplying the total gallons (8.4) by the unknown price per gallon (x) and setting it equal to the total cost ($23.94). Think about it: If we multiply the number of gallons by the price per gallon, we should get the total cost. This equation reflects the fundamental relationship between these values. This one's a strong contender!

Option D: $x / 8.4 = 23.94$

Finally, let's look at this equation. It suggests that if we take the unknown price per gallon (x) and divide it by the total gallons (8.4), we'll get the total cost ($23.94). This doesn't make much sense either. Dividing the price per gallon by the number of gallons doesn't logically lead us to the total cost. So, we can rule this one out.

The Correct Equation Revealed

After carefully examining each option, it's clear that Option C: $8.4x = 23.94$ is the correct equation. This equation accurately represents the relationship between the total gallons, the price per gallon, and the total cost. It aligns perfectly with our understanding of how these values interact.

To recap, we knew that the total cost is equal to the price per gallon multiplied by the number of gallons. Equation C puts this relationship into a mathematical form that we can use to solve for the unknown price per gallon.

Solving for the Price per Gallon

Okay, so we've identified the correct equation, but let's take it a step further. How would we actually solve for the price per gallon (x) using this equation? It's a simple algebraic step that reinforces our understanding of the problem.

We have the equation $8.4x = 23.94$. To isolate x (the price per gallon), we need to undo the multiplication by 8.4. We do this by dividing both sides of the equation by 8.4:

$8. 4x / 8.4 = 23.94 / 8.4$

This simplifies to:

$x = 23.94 / 8.4$

Now, we just need to perform the division:

$x = 2.85$

So, the price per gallon of gas is $2.85. We've not only found the correct equation but also solved it to find the actual price. Awesome!

Why This Matters: Real-World Math

You might be wondering, "Why is this important?" Well, these kinds of problems come up in everyday life. Whether you're calculating the cost of gas, figuring out grocery prices, or budgeting for a trip, understanding how quantities and prices relate is super useful. This exercise with Evelyn's gas purchase is a perfect example of how math helps us make sense of the world around us.

Think about it: If you know the price per gallon and how many gallons your car holds, you can estimate how much it will cost to fill up your tank. If you're comparing prices at different gas stations, you can quickly calculate the total cost based on their per-gallon prices. These skills are practical and empower you to make informed decisions.

Key Takeaways

Before we wrap up, let's highlight the key things we've learned in this gas price adventure:

• Understanding the Relationship: The total cost is the product of the price per unit (in this case, price per gallon) and the quantity (number of gallons).
• Translating Words to Equations: We can take a real-world scenario and translate it into a mathematical equation that represents the situation.
• Solving for the Unknown: Once we have the equation, we can use algebraic techniques to solve for the unknown variable (in this case, the price per gallon).
• Real-World Application: These math skills are valuable in everyday situations, helping us make informed decisions about spending and budgeting.

Wrapping Up

So, there you have it! We've successfully navigated the gas price problem, identified the correct equation, and even solved for the price per gallon. This exercise demonstrates how math isn't just something you learn in a classroom; it's a tool that helps us understand and interact with the world around us. Next time you're at the gas pump, you'll have a deeper appreciation for the math behind the prices!

Keep practicing, keep exploring, and keep those math skills sharp. You never know when they'll come in handy. Until next time, happy calculating!