Problem 51 - Algebra 1

Question

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. Use mental math to solve the equation.

Step-by-Step Solution

Answer

21 magazine subscriptions need to be sold to raise $315.

Step 1: Understand the problem

The task is to figure out how many $15 subscriptions need to be sold in order to raise $315.

Step 2: Identify the relevant information

Every magazine subscription is sold for $15, and the total amount of money that needs to be raised is $315.

Step 3: Formulate the mathematical equation

The equation that represents this problem can be written as \(15x = 315\), where x represent the number of subscriptions to be sold.

Step 4: Solve the equation

To find out the number of subscriptions, divide the total amount of money that needs to be raised by the price of each subscription, i.e., \(x = 315/15\).

Step 5: Find the solution

Divide 315 by 15 to find the solution, i.e., x = 21.

Key Concepts

Algebra Basics

Algebra is all about finding the unknown values in mathematical expressions. In this problem, we are dealing with an equation, which is a fundamental concept in algebra. Equations show a relationship between different quantities. Here, the equation is written as \(15x = 315\). This equation says that 15 times a certain number \(x\) equals 315.

To solve it, you need to determine what number multiplied by 15 gives 315. Algebra often involves operations like addition, subtraction, multiplication, and division to isolate the unknown variable. It is critical to thoroughly understand how these operations interact to break down the relationships and solve for the unknown variable in equations.

Practice different problems to become familiar with various algebraic techniques. Solving simple equations mentally is a great way to boost your understanding and self-assurance.

Equation Solving Made Simple

Equation solving is a key part of algebra that involves finding the value of the unknown variable. Here, we started with the equation \(15x = 315\), which represents our problem. The objective is to solve for \(x\), which symbolizes the number of magazine subscriptions needed.

To find \(x\), you simply divide both sides of the equation by 15. This step reveals the exact number of subscriptions required. So, \(x = \frac{315}{15}\), which then simplifies to \(x = 21\). Division is the reverse of multiplication, and using it helps isolate \(x\) on one side of the equation.

It is crucial to keep equations balanced, which means performing the same operation on both sides. This ensures that we maintain equality as we work through solving the equation. Approaching equation solving with precision can significantly enhance your mathematical reasoning and efficiency.

Boosting Problem-Solving Skills

Problem-solving skills are essential for tackling mathematical exercises and beyond. They involve strategies to understand and solve challenges systematically. With this magazine subscription problem, effective problem-solving started with comprehending the question thoroughly.

Breaking down the problem into manageable parts, like identifying known and unknown quantities, is vital. Calculating the number of magazine subscriptions needed requires a step-by-step approach:

• Understand the problem and what it is asking
• Collect all relevant information and data
• Formulate a mathematical equation to represent the scenario
• Solve the equation accurately

Cultivating these skills improves confidence and ability to apply mathematical concepts to real-world situations. Always double-check your solutions to ensure accuracy and learn from any missteps along the way. Practice regularly to enhance your problem-solving prowess.