Problem 44 - Prealgebra

Question

cost of Apples Mary is purchasing 12 apples. Each apple weighs 4 oz. If the cost of the apples is $$ 1.50$ a pound, how much will Mary pay?

Step-by-Step Solution

Answer

Mary will pay $4.50 for the apples.

Step 1: Convert the Weight to Pounds

The first step is to understand that there are 16 oz in a pound. Since each apple weighs 4 oz, calculate how many ounces 12 apples weigh. Multiply 12 (the number of apples) by 4 oz (the weight per apple): \[ \text{Total weight in oz} = 12 \times 4 = 48 \text{ oz} \]Now, convert this total weight from ounces to pounds by dividing by 16 (since there are 16 oz in a pound):\[ \text{Total weight in pounds} = \frac{48}{16} = 3 \text{ pounds} \]

Step 2: Calculate the Total Cost

With the total weight of apples in pounds calculated, we now determine the total cost. Given that the price is \(1.50 per pound, multiply the weight in pounds by the cost per pound:\[ \text{Total cost} = 3 \times 1.50 = 4.50 \]Thus, Mary will pay \)4.50 for the apples.

Key Concepts

Convert ounces to pounds

Converting ounces to pounds is a common task when dealing with purchases, especially in the United States where both measurements are frequently used. To convert ounces to pounds, remember that there are 16 ounces in a single pound. This means you can convert by dividing the number of ounces by 16.
For example, if you have a total weight of 48 ounces, you convert this to pounds by using the formula:\[\text{Total weight in pounds} = \frac{48}{16} = 3 \text{ pounds}\]Here are the steps in a nutshell:

• Calculate the total number of ounces by multiplying the quantity by the weight per item.
• Divide the total ounces by 16 to find the equivalent weight in pounds.

This conversion is crucial because many products are priced per pound and not per ounce.

Calculation of total cost

Calculating the total cost involves determining how much you need to pay for a certain amount based on price per unit weight. In our example, the apples are priced at \(1.50 per pound. Once we know the total weight in pounds, we can find out how much Mary will pay by multiplying the total weight by the price per pound.
The formula looks like this:\[\text{Total cost} = \text{Total weight in pounds} \times \text{Price per pound}\]In practical terms, if the total weight of the apples is 3 pounds, and the price is \)1.50 per pound, the calculation will be:\[\text{Total cost} = 3 \times 1.50 = 4.50\]This results in Mary paying $4.50 for the 12 apples.To ensure accuracy:

• Always double-check your weight and unit conversions.
• Multiply the pounds by the price per pound only after confirming the conversion from ounces or any other measurement.

Unit price analysis

Unit price analysis helps consumers compare prices regardless of packaging size or weight. Understanding how to analyze unit prices will allow you to determine the best deals.
A unit price tells you the cost of one unit of the item, which in our exercise is in pounds. Calculating a unit price is straightforward when the unit and the cost per unit are provided. In our apples example, we start with a known unit price: $1.50 per pound.
The purpose of analyzing unit prices is to:

• Ensure you are getting the best value for your money.
• Help you budget more effectively by estimating costs upfront.
• Allow you to compare similar products priced differently due to packaging or brand.

Understanding how unit price analysis works enhances your financial literacy and purchasing decisions. It enables you to make informed choices and maximize your buying power.