Problem 62 - Algebra 1

Question

To promote sales, a grocery store advertises bananas for \(\mathbf{S} . \mathbf{2 5}\) per pound. The store loses \(\mathbf{S} . \mathbf{1 1}\) on each pound of bananas it sells. The store sells 2956 pounds of bananas. How much money does the store lose on banana sales?

Step-by-Step Solution

Answer

The store loses $325.16 on banana sales.

Step 1: Identify and Understand the Given Units

In this problem, the store loses $0.11 on each pound of bananas it sells. Therefore, the value per pound is -$0.11. Also given, the store sells 2956 pounds of bananas.

Step 2: Multiply the Amount of Money Lost per Pound by the Total Pounds of Bananas Sold

In this step, the calculation needs to multiply the amount of money lost per pound by the total pounds of bananas sold. So, - $0.11 * 2956 pounds.

Step 3: Calculate the Total Money Lost on Banana Sales

Using the multiplication from step 2, the total amount of money the store lost on banana sales is - $0.11 * 2956 = -$325.16.

Key Concepts

Multiplication of Decimals

Multiplying decimals is a fundamental skill in math that's widely applicable, whether in everyday life, such as handling money, or in various academic fields. To master this concept, let's take a closer look at the process used in our grocery store problem.

First, align the numbers by their decimal points. Then, proceed as if you were multiplying whole numbers. Don't forget to count the total number of decimal places in the factors, as your answer should have the same number of decimal places. In the banana example, we had to multiply \(0.11 (a decimal with two places) by 2956 (a whole number), which resulted in 325.16. However, since the store loses money, the result is negative: -\)325.16.

• Align decimal points
• Multiply as with whole numbers
• Count decimal places for the product
• Ensure the sign (positive or negative) is accurate

Solving Word Problems

Word problems turn real-world scenarios into math equations, requiring us to extract and compute numerical information. They often seem intimidating, but a structured approach can simplify them. Take our grocery store's scenario. The crucial steps are identifying the key pieces of information and determining the operation required—in this case, multiplication.

To solve these problems, follow these steps:

• Read the problem carefully to understand the context and the question.
• Identify the numbers and their units (e.g., pounds, dollars).
• Determine the mathematical operation needed between the identified numbers.
• Write down the equation, solve it, and check if the answer makes sense within the problem's context.

When working on word problems, pay special attention to the units and whether the problem is asking for a total, a difference, or a comparative quantity. This will guide you to apply the correct mathematical operation.

Understanding Unit Price

Unit price refers to the cost for a single unit of measure of a product or service. In daily life, it helps us determine the 'real' price of a product and facilitate price comparisons. In our exercise, the unit price is the amount the grocery store loses on each pound of bananas, which is $0.11.

Calculating the unit price loss is as simple as looking at the cost incurred for one unit, and this figure can help in further calculations, like finding the total loss.

• Identify the cost associated with one unit.
• Multiply the unit cost by the number of units to find the total cost or loss.
• Use this information to make informed decisions or solve problems related to pricing.

Understanding unit price not only aids in solving textbook questions but also prepares you for making savvy decisions as a consumer or a business owner.