Problem 67 - Prealgebra

Question

Perform the indicated operations. If fish costs \(\$ 6.00\) per pound, find the cost of 15 pounds.

Step-by-Step Solution

Answer

The total cost for 15 pounds of fish is $90.00.

Step 1: Understand the Problem

We need to find the total cost of 15 pounds of fish if the price per pound is $6.00.

Step 2: Identify the Needed Operation

To find the total cost, we must multiply the number of pounds by the price per pound.

Step 3: Set Up the Multiplication Equation

The equation to find the total cost is given by \( \text{Total Cost} = \text{Number of Pounds} \times \text{Cost per Pound} \).

Step 4: Substitute Values into the Equation

Substitute the known values into the equation: \( \text{Total Cost} = 15 \times 6 \).

Step 5: Perform the Multiplication

Calculate the product: \( 15 \times 6 = 90 \).

Step 6: State the Total Cost

The total cost for 15 pounds of fish at $6.00 per pound is $90.00.

Key Concepts

Understanding Multiplication in Cost Calculation

When calculating costs for items priced per unit, multiplication is the key operation. This is because you're essentially adding the unit price to itself repeatedly. For instance, if you buy several pounds of fish, each at a specific price, you add the price for each pound bought. Rather than adding the cost repeatedly, multiplication streamlines this process. This efficient operation not only saves time but also reduces the possibility of arithmetic errors. In our example:

• Each pound of fish costs \(6.00.
• You purchase 15 pounds of fish.

The multiplication equation, therefore, is: \[\text{Total Cost} = 15 \times 6\]Instead of adding \)6.00 fifteen times, the multiplication does it in one step.

Applying Problem-Solving Skills

Problem-solving in mathematics often involves understanding what you're being asked to find. It also involves selecting the right operations to use. Let's dive deeper into how we used problem-solving for this cost calculation. 1. **Clarifying the Objective**: We start by clearly stating what needs to be determined. In this case, it's the total cost for 15 pounds of fish. 2. **Choosing the Correct Operation**: Since we have a per-unit cost ($6.00 per pound) and a total quantity (15 pounds), multiplication is the appropriate operation. 3. **Setting Up the Equation**: Creating an equation helps organize information and simplifies the problem. Here, our equation is based on the number of pounds and the per-pound cost. 4. **Performing the Calculation**: After setting up the equation, the next step is to substitute with our known quantities and multiply. The product here is 90, meaning $90.00 is the total cost. By following these structured steps, solving such problems becomes manageable and systematic.

Calculating Costs: From Equation to Total

Understanding how to calculate total costs using a multiplication equation can be very practical. Here’s why it's important not just for students but also in everyday life when dealing with budgets, shopping, or business.The equation for calculating costs is straightforward: \[\text{Total Cost} = \text{Quantity} \times \text{Unit Price}\]In the context of our exercise:

• The quantity of fish is 15 pounds.
• The unit price is \(6.00 per pound.

By multiplying these two, we find the total cost:\[15 \times 6 = 90\]Thus, \)90.00 is the total amount needed to purchase 15 pounds of fish at the given price.Cost calculation via multiplication is a fundamental arithmetic skill. It applies broadly, from personal finance to commercial transactions, ensuring not only accuracy but also efficiency in determining expenses.