This simple equation, "the product of 7 and j is 91," might seem basic, but it forms the foundation of understanding algebraic concepts. This post will break down how to solve this equation, explain the underlying mathematical principles, and provide examples of similar problems to solidify your understanding.
Understanding the Problem
The phrase "the product of 7 and j" means 7 multiplied by j. We can represent this mathematically as 7j or 7 * j. The problem states that this product equals 91. Therefore, we can write the equation as:
7j = 91
Our goal is to find the value of 'j'.
Solving for 'j'
To isolate 'j' and find its value, we need to perform the inverse operation of multiplication, which is division. We'll divide both sides of the equation by 7:
7j / 7 = 91 / 7
This simplifies to:
j = 13
Therefore, the value of 'j' that satisfies the equation is 13.
Verification
To verify our solution, we can substitute 'j' with 13 back into the original equation:
7 * 13 = 91
This confirms that our solution is correct.
Similar Problems and Applications
This type of problem is fundamental to algebra and has wide-ranging applications in various fields. Here are some similar examples:
- Example 1: The product of 5 and x is 60. Find the value of x. (Solution: x = 12)
- Example 2: If 8 times y equals 72, what is the value of y? (Solution: y = 9)
- Example 3: A rectangle has a length of 7 units and an area of 91 square units. What is the width of the rectangle? (Solution: Width = 13 units, using Area = Length x Width)
These examples demonstrate the practical application of solving for an unknown variable in a simple algebraic equation. Understanding this fundamental concept is crucial for progressing to more complex mathematical problems.
Conclusion
Solving the equation "the product of 7 and j is 91" involves understanding the concept of algebraic equations and applying the inverse operation of division to isolate the unknown variable. By mastering this simple equation, you build a strong foundation for more advanced algebraic concepts and their real-world applications. Remember, practice is key to mastering these skills!
