Problem 38 - Prealgebra

Question

cost of Steak Mike is purchasing eight top sirloin steaks. The meat costs $$ 4.00$ per pound, and each steak weighs 1 Ib 4 oz. What is the total cost of the steaks?

Step-by-Step Solution

Answer

The total cost of the steaks is $40.00.

Step 1: Convert oz to lb

First, we need to convert the weight of each steak from pounds and ounces to pounds alone. Since there are 16 ounces in a pound, 4 ounces is equal to \( \frac{4}{16} = 0.25 \) pounds. Therefore, each steak weighs \( 1 + 0.25 = 1.25 \) pounds.

Step 2: Calculate total weight

Next, we calculate the total weight of all steaks combined. Since there are 8 steaks each weighing 1.25 pounds, the total weight is \( 8 \times 1.25 = 10 \) pounds.

Step 3: Calculate total cost

Finally, to find the total cost of the steaks, multiply the total weight by the cost per pound. Therefore, the total cost is \( 10 \times 4.00 = 40.00 \) dollars.

Key Concepts

Understanding Unit Conversion

In many real-world situations, you need to convert between different units of measurement. This is particularly important when dealing with weights or measures given in both pounds and ounces, as they are common in recipes or when buying food items. To convert ounces (oz) to pounds (lb), remember that there are 16 ounces in a pound. So, if you have 4 ounces, you convert it by dividing by 16. For example, \( \frac{4}{16} = 0.25 \) pounds. This means that 4 ounces is equal to 0.25 pounds. When dealing with mixed units like pounds and ounces, first convert the ounces to pounds. Then, add this to the pounds portion. For example, if a steak weighs 1 pound 4 ounces, convert the 4 ounces to pounds (0.25 pounds) and then add it to the 1 pound, resulting in a total weight of 1.25 pounds. Breaking down the weights into a single unit simplifies calculations, especially when you need to perform multiplication or addition later on.

Multiplication: Finding Total Weight

Once you have converted all measurements to the same unit, you can easily find the total weight (or measure) by using multiplication. Multiplication helps in finding the cumulative effect of a single unit over several items. In our steak scenario, after converting each steak's weight to pounds, you multiply by the number of steaks. Here's a quick breakdown:

• The weight of each steak is 1.25 pounds.
• There are 8 steaks in total.

To find the total weight, multiply: \( 1.25 \times 8 = 10 \) pounds. This means all steaks together weigh 10 pounds. Multiplication here provides an efficient way to handle repeated addition, making it quicker to find totals. Understanding and applying multiplication helps in various situations from calculating total weights to determining the required resources in larger batches.

Mastering Cost Calculation

Once you know the total weight of your items, cost calculation becomes straightforward. It involves multiplying the total weight by the cost per unit weight. This step helps you determine the total expense, especially useful when budgeting or comparing price options.

• Total weight of steaks: 10 pounds
• Cost per pound: \(4.00

Now, multiply the total weight by the cost per pound: \( 10 \times 4.00 = 40.00 \) dollars.This means you will spend \)40.00 on those steaks. Cost calculation is essential in everyday finances, helping to ensure you stay within budget and make informed purchasing decisions. Understanding how to calculate total costs equips you to handle a variety of scenarios, from grocery shopping to cost estimation in larger projects.