Problem 43 - Algebra 1

Question

Match the real-life problem with an equation. Then solve the problem. A. \(x+15=7\) B. \(15-x=7\) C. \(15+7=x\) D. \(x+15=-7\) There are 15 members of a high school band brass section. After graduation there are only 7 members. How many members graduated?

Step-by-Step Solution

Answer

8 members graduated from the high school band.

Step 1: Match the situation with an equation

The situation describes the number of members decreasing from 15 to 7 due to graduation. This reflects a subtraction operation, so the equation should involve subtraction. Out of the presented options, B. \(15-x=7\) matches the real-life problem.

Step 2: Solve the matching equation

To find the number of members graduated, solve equation B. \(15-x=7\) for \(x.\) The solution is obtained by subtracting 7 from both sides of the equation. In other words, \(x\) equals \(15 - 7\).

Step 3: Calculate the value of x

By performing the subtraction operation, it is found that \(x = 15 - 7 = 8\). So, 8 members graduated from the high school band.

Key Concepts

subtraction

Subtraction is one of the fundamental operations in mathematics. It involves taking one number away from another. In our equation solving example, the number of members in the band decreased from 15 to 7, signifying a subtraction process. This can be thought of as asking, "How many need to be removed to reach a certain amount?"Subtraction in equations:

• Typically presented as: "A - B = C," where you need to find one of the numbers.
• It is an essential skill for high school math, aiding in solving many real-life problems.

In the case of our exercise, the equation for the process of subtraction was given as \(15 - x = 7\). The goal was to find the value of \(x\) that correctly represents the number of graduating members.

real-life problem

Solving real-life problems using equations is a powerful application of mathematics. In real-life settings, chemistry, finance, and even music can present situations where math is needed. Our high school band scenario is a perfect example.In this situation:

• We had a starting count of 15 band members.
• After graduation, only 7 remained.
• We wanted to determine how many members graduated.

Identifying the subtraction equation from the complications of real-life scenarios like this helps in making logical and quantitative decisions. In this case, matching the situation with the equation \(15 - x = 7\) provided a clear path to finding our solution, making it understandable and manageable.

high school mathematics

High school mathematics lays the foundation for solving both theoretical and practical problems. Understanding equations like the one in the exercise bridges academic concepts with real-world applications. This exercise serves as a typical high school-level problem requiring students to engage critically with mathematical concepts. Educational importance of this exercise:

• It teaches students to translate word problems into mathematical equations.
• Involves logic and deduction to correctly select the form of the equation.
• Reinforces basic concepts such as subtraction within an algebraic context.

By mastering these skills, students can feel confident tackling more complex mathematical challenges later in their educational journey. In this scenario, understanding that a simple action like subtracting members due to graduation can be represented mathematically is a powerful learning experience.