Problem 51 - Algebra 1: Concepts and Skills

Question

MAIL DELIVERY Each household in the United States receives about 676 pieces of junk mail per year. If there are 52 weeks in a year, then about how many pieces of junk mail does a household receive per week? HINT: Let \(x=\) the number of pieces of junk mail received per week. Solve the equation \(52 x=676\)

Step-by-Step Solution

Answer

A household in the United States receives approximately 13 pieces of junk mail per week.

Step 1: Identify the given values

In this problem, it is given that each household in the United States receives about 676 pieces of junk mail per year. And also it is given that a year has 52 weeks.

Step 2: Formulate the equation

Let \(x\) be the number of pieces of junk mail received per week. So, the total junk mail received in a year would be the junk mail received per week times the number of weeks in a year. Therefore, the equation will be \(52x = 676\).

Step 3: Solve the equation

To solve for \(x\), divide both sides of the equation by 52, which gives \(x = 676 / 52\).

Step 4: Compute for the value of \(x\)

By calculating the right side of the equation, it gives \(x = 13\). This means that a household receives approximately 13 pieces of junk mail per week.

Key Concepts

Division

Division is a fundamental operation in mathematics that helps us split a quantity into equal parts or groups. When solving equations like the one in our exercise, division becomes an essential step to isolate the variable and find its value. In our mail problem, we're given a yearly total of junk mail that we need to break down into weekly portions.

• To divide means taking a total quantity and separating it into equal parts.
• The division in the equation is expressed as \(52x = 676\), where you divide both sides by 52.
• Performing the division, \(x = \frac{676}{52}\) gives you the number of junk mails per week.

This concept resembles distributing candies equally among a group of friends or figuring out how much money each person pays when splitting a bill. Each time you divide, you're aiming to determine how much one part (or group) gets out of the total.

Problem Solving

Problem solving is like unfolding layers of a mystery where each layer brings you closer to the solution. It involves understanding the problem, coming up with a plan, solving the equation, and then checking if the solution makes sense. In our junk mail problem, these are the steps you'll follow:

• Understanding the Problem: Recognize you need to find how many pieces of junk mail are received per week.
• Planning: Use the equation \(52x = 676\) to express what you're trying to find.
• Solving the Equation: Break down 676 pieces per year into weekly segments by performing division.
• Verify: Double-check your final result to ensure it fits the problem's requirement.

Each step in problem solving helps clear the path from confusion to clarity, making it a powerful tool in mathematics and real life.

Formulating Equations

Formulating equations is about translating a real-world scenario into a mathematical statement. It's the bridge that connects the story of a problem with the tools needed to solve it. In the mail delivery exercise, we start by identifying key quantities and their relationships based on the problem's context.

• Identify Important Quantities: Recognize the yearly total of 676 pieces of junk mail and the 52 weeks.
• Define Variables: Set \(x\) as the unknown variable representing weekly junk mail pieces.
• Create the Equation: Form the equation \(52x = 676\) to represent the relationship between total yearly mail and weekly distribution.

By formulating an equation, you create a clear and solvable pathway, allowing you to use mathematical operations to find a missing piece of information—a crucial skill in mathematics and beyond.