Problem 37 - Prealgebra

Question

cost of Fish Fredrick is purchasing four whole salmon. The fish cost $$ 4.00$ per pound, and each weighs 6 lb 8 oz. What is the cost of the fish?

Step-by-Step Solution

Answer

The total cost for the fish is $104.

Step 1: Convert ounces to pounds

Each salmon weighs 6 lb 8 oz. First, convert 8 oz into pounds. Since 1 pound is equal to 16 ounces, we divide 8 oz by 16 oz/lb to get the equivalent in pounds: \( \frac{8}{16} = 0.5 \) pounds.

Step 2: Calculate total weight per salmon

Add the converted ounce pounds to the whole pounds to find the total weight of one salmon in pounds. So, each salmon weighs \( 6 + 0.5 = 6.5 \) pounds.

Step 3: Calculate the cost per salmon

The price is $4.00 per pound. Therefore, the cost for one salmon is \( 6.5 \times 4 = 26 \) dollars.

Step 4: Calculate the cost for all the salmon

Since Fredrick is purchasing four salmon, multiply the cost per salmon by 4. Thus, \( 26 \times 4 = 104 \) dollars.

Key Concepts

Weight Conversion

When dealing with the weight of objects, such as fish, knowing how to convert between different units of measurement is crucial. This concept involves transforming ounces into pounds, which is common in weight-related calculations in the United States. A solid understanding of this conversion can simplify many real-world problems.

To convert ounces to pounds, remember that there are 16 ounces in a pound. This means that to find how many pounds a certain number of ounces is, you would divide the ounces by 16. For example, converting 8 ounces into pounds could be done by calculating \( \frac{8}{16} = 0.5 \) pounds.

Whenever you're converting weights, it's essential to ensure all measurements are in the same unit, especially before performing any calculations, such as finding out the total weight or costing. Knowing this helps provide consistent and accurate results, avoiding any errors in the final calculation.

Cost Calculation

Once the weights have been correctly converted into a common unit, the next step is often to calculate the cost based on this weight. This process is straightforward but crucial for budgeting and purchasing decisions.

To determine the cost of an item sold by weight, you can multiply the total weight of the item by the price per pound. In our example with the salmon fish, each one weighs 6.5 pounds after converting ounces to pounds. With a cost of \(4.00 per pound, the calculation for one salmon is \(6.5 \times 4 = 26\) dollars.

To get the total cost when buying multiple items, you multiply the cost per item by the total number of items. Fredrick, buying four salmon at \)26 each, will spend a total of \(26 \times 4 = 104\) dollars. By following this straightforward multiplication process, you can ensure all items are priced accurately and within budget.

Pounds and Ounces

Understanding pounds and ounces is fundamental to working with weights and measures in countries that use the imperial system. These units are often used together to provide precise measurements.

A pound is a larger unit of weight, and within it, there are 16 smaller units known as ounces. For measurements where precision matters, the combination of pounds and ounces allows for expressing weights accurately, such as 6 lb 8 oz.

To add weights given in pounds and ounces:

• First, convert the ounces part into a fractional pound.
• Then, add this to the given whole pounds.

So, 8 ounces is converted to \(0.5\) pounds, and when added to 6 pounds, it becomes \(6 + 0.5 = 6.5\) pounds. This ensures all weight the calculations are in a single unit, simplifying processes like cost calculation.

This understanding helps eliminate confusion and errors in measurement tasks, especially when dealing with inventory, cooking, and other practical applications where weights need accurate representation.