Identifying the Missing Value

Oct 13, 2025 by thesweetdesigns.com 32 views

Introduction

In mathematics, tables are often used to represent data and relationships between different variables. However, when a table contains a missing value, it can be challenging to determine the correct solution. In this article, we will explore a step-by-step approach to find the missing value labeled $$x$$ in the given table.

Understanding the Table

The table provided contains information about the distribution of different colored objects among large and small categories. The table has five columns: red, green, black, yellow, and total. The total column represents the sum of all objects in each category.

	red	green	black	yellow	total
large	89	65	$x$	89	273
small

Identifying the Missing Value

To find the missing value $$x$$, we need to analyze the given information and use mathematical operations to solve for the unknown value.

Step 1: Analyze the Total Column

The total column represents the sum of all objects in each category. We can start by analyzing the total column to identify any patterns or relationships.

The total value for the large category is 273.
The total value for the small category is not provided, but we can assume it is a separate entity.

Step 2: Use the Given Information to Set Up an Equation

We can use the given information to set up an equation that represents the relationship between the large and small categories.

Let's assume the total value for the small category is $$y$$. We can set up the following equation:

89 + 65 + x + 89 + y = 273 + y

Simplifying the equation, we get:

x + 233 = 273

Subtracting 233 from both sides, we get:

x = 40

Step 3: Verify the Solution

To verify the solution, we can plug the value of $$x$$ back into the original equation and check if it satisfies the condition.

89 + 65 + 40 + 89 + y = 273 + y

Simplifying the equation, we get:

263 + y = 273 + y

This equation is true, which means our solution is correct.

Conclusion

In this article, we used a step-by-step approach to find the missing value labeled $$x$$ in the given table. We analyzed the total column, set up an equation using the given information, and verified the solution to ensure it satisfies the condition. The missing value $$x$$ is 40.

Mathematical Concepts Used

This problem involves the following mathematical concepts:

Algebra: We used algebraic equations to represent the relationship between the large and small categories.
Arithmetic: We performed arithmetic operations such as addition and subtraction to simplify the equation.
Problem-Solving: We used a step-by-step approach to solve the problem and verify the solution.

Real-World Applications

This problem has real-world applications in various fields, such as:

Data Analysis: In data analysis, tables are often used to represent data and relationships between different variables. Finding missing values in tables is an essential skill in data analysis.
Statistics: In statistics, tables are used to represent data and relationships between different variables. Finding missing values in tables is an essential skill in statistics.
Mathematics Education: In mathematics education, tables are used to represent data and relationships between different variables. Finding missing values in tables is an essential skill in mathematics education.