Trail Mix Equation: Calculate Price Per Pound

Let's break down how to calculate the price per pound of Marion's trail mix! This is a classic problem that involves understanding how to combine different costs and quantities. We'll walk through it step by step so you can see how to set up the equation. If you're into outdoor activities like camping, having the perfect trail mix is a must, and knowing how to budget for it is even better.

Understanding the Problem

The core of this problem revolves around figuring out the average cost per pound of the final trail mix. Marion is mixing two ingredients: granola and raisins. We know the weight and cost per pound of each ingredient. To find the overall price per pound, we need to consider the total cost of all ingredients and the total weight of the mix. It's like when you're at the grocery store, comparing prices of different items – you want to know what you're really paying for each unit of the product.

To effectively address this, let's first nail down the individual costs. Marion purchases 3 pounds of granola, each pound costing $3. So, the total expense for granola is simply 3 pounds multiplied by $3 per pound. Similarly, she buys 0.75 pounds of raisins at $2 per pound, so the total cost for raisins is 0.75 pounds times $2 per pound. Once we have these individual costs, we can add them together to find the total expenditure on all ingredients. This total cost is a crucial piece of the puzzle.

Next, we need to figure out the total weight of the trail mix. This is straightforward: we just add the weight of the granola (3 pounds) to the weight of the raisins (0.75 pounds). This gives us the total quantity of trail mix Marion is making. Now we have two key figures: the total cost of the ingredients and the total weight of the mix. The final step is to combine these two figures to find the price per pound, which we'll do using a simple division.

Calculating the Total Cost

Okay, let's dive into the nitty-gritty and calculate the total cost of Marion's ingredients. Remember, she's buying two items: granola and raisins. We need to figure out how much she's spending on each before we can add them up. Think of it like adding up the prices on your shopping list – you look at each item individually and then combine the costs.

First up is the granola. Marion is getting 3 pounds of this, and it costs $3 for each pound. To find the total cost, we simply multiply the quantity (3 pounds) by the price per pound ($3). This gives us 3 * $3 = $9. So, Marion is spending $9 on granola. It's crucial to get these individual costs right because they form the foundation of our overall calculation. A small mistake here can throw off the final answer, so let's double-check our work as we go.

Next, let's tackle the raisins. She's buying 0.75 pounds, and they cost $2 per pound. Again, we multiply the quantity (0.75 pounds) by the price per pound ($2). This gives us 0.75 * $2 = $1.50. So, the raisins are costing her $1.50. Now we have the individual costs for both the granola and the raisins. It’s like we're building a financial snapshot of Marion's trail mix ingredients!

Now that we know the individual costs, we can find the total cost. We add the cost of the granola ($9) to the cost of the raisins ($1.50). This gives us $9 + $1.50 = $10.50. So, Marion is spending a total of $10.50 on the ingredients for her trail mix. This total cost is a key number – it's the numerator in our eventual calculation of the price per pound. We’re getting closer to solving the puzzle!

Determining the Total Weight

Now that we've figured out the total cost of the ingredients, the next step is to determine the total weight of the trail mix. This is a much simpler calculation than figuring out the cost, but it's equally important. Think of it like measuring ingredients for a recipe – you need the right amounts to get the proportions correct.

Marion is using two ingredients in her mix: granola and raisins. We know she's using 3 pounds of granola and 0.75 pounds of raisins. To find the total weight, we just need to add these two amounts together. It's a straightforward addition problem, but let’s make sure we get it right.

So, we add 3 pounds (granola) to 0.75 pounds (raisins). This gives us 3 + 0.75 = 3.75 pounds. Therefore, the total weight of Marion's trail mix is 3.75 pounds. This number is crucial because it will be the denominator in our calculation of the price per pound. Remember, we're trying to find out how much each pound of the final mix costs, so we need to know the total weight to divide the total cost appropriately.

Getting the total weight correct is essential for the final calculation. It’s like knowing the total yield of your recipe – it tells you how much you're making overall. With the total weight in hand, we're now just one step away from figuring out the price per pound. We've got the total cost and the total weight; now it's time to put them together.

Setting Up the Equation

Alright, guys, this is where we bring everything together! We've calculated the total cost of the ingredients and the total weight of the trail mix. Now, we need to set up the equation that will give us the price per pound. This is like the grand finale of our math problem – we're taking all the pieces we've assembled and putting them in the right order to get our answer. Think of it as writing the recipe instructions after gathering all the ingredients.

Remember, we want to find the price per pound, which means we need to divide the total cost by the total weight. This is a fundamental concept in figuring out unit prices – you're essentially spreading the total cost evenly across each pound of the mix. The equation we'll use is simple: Price per pound = Total cost / Total weight. It’s a basic formula, but it's incredibly useful in everyday situations, from grocery shopping to budgeting for a camping trip.

We know the total cost is $10.50 (from our earlier calculations) and the total weight is 3.75 pounds. So, we can plug these numbers into our equation: Price per pound = $10.50 / 3.75 pounds. This is the equation that will give us the price per pound of Marion's trail mix. The equation itself is the key to solving the problem – it lays out the mathematical relationship between the cost, weight, and price per pound.

So, to recap, the equation we use to find the price per pound of the trail mix is $10.50 / 3.75. This equation clearly shows how we are distributing the total cost across the total weight to find the unit price. Now, you could actually perform the division to get the exact price per pound, but the question asked for the equation, and we've got it! We've successfully set up the problem and can confidently say we know how to find the price per pound of the trail mix.