Solving Mathematical Equations for A, B, and C: A Comprehensive Guide

In this article, we will solve a specific mathematical equation involving variables A, B, and C. Our goal is to find the value of C given the conditions provided. This is a breakdown of the problem and the step-by-step solution, making it easy to understand for anyone with a basic understanding of algebra.

Introduction to the Problem

The problem statement is simple yet engaging: what is the value of C in the equation 90% of A equals 30% of B, and B is C times A. Let's break down the problem step by step to reach the final solution.

Step-by-Step Solution

Given Equations

90% of A 30% of B B C times A

Solving for B

Starting with the first equation, we can write it in a more convenient form:

90/100 A 30/100 B

By simplifying the fractions, we get:

9A/10 3B/10

Since the denominators are the same, we can equate the numerators:

9A 3B

Dividing both sides by 3, we get:

3A B

Given B in Terms of C

The second equation tells us that B can be expressed as C times A:

B C * A

Since we know that B 3A, we can substitute 3A for B in the equation B C * A:

3A C * A

Dividing both sides by A (assuming A is not zero), we get:

C 3

Finding the Value of C

With this step, we have determined that C equals 3. Now, we need to find the value C in terms of A. Given that C is equivalent to 300%, we can calculate the value of C in relation to A:

C 300% of A or 300/100 A 3A

Therefore, the value of C is 300.

Conclusion

Through a series of algebraic manipulations, we have derived the value of C as 300. This problem demonstrates the importance of breaking down complex equations into simpler terms and using basic algebra to find solutions.

Practical Applications

This type of problem-solving is not only relevant in academic contexts but also in real-world applications. Understanding how to manipulate and solve equations involving percentages and variables can be invaluable in fields such as finance, economics, and engineering.

Further Reading

Algebraic Equations Percentage Calculations in Math Variable Manipulation in Algebra

By exploring these further reading topics, you can deepen your understanding of how to solve similar types of mathematical problems.

FAQs

What is the significance of solving basic algebraic equations? Understanding algebraic equations is crucial for advanced mathematics and practical problem-solving in various fields. It helps build a strong foundation in mathematics. It aids in critical thinking and logical reasoning. Can you provide more examples of similar algebraic problems? Solving for multiple variables in simultaneous equations. Working with proportions and ratios. Using algebra to solve real-world problems in business and science. How to prepare for algebraic problem-solving? Practice solving a variety of algebraic equations. Use online resources and tutorials to supplement classroom learning. Engage in problem-solving sessions with peers or mentors to enhance understanding.

References

Math Is Fun - Algebra Khan Academy - Algebra Math Planet - Algebra 1