Solving a Mathematical Problem: Thrice a Number Increased by 1 is 64

When faced with a problem like 'thrice a number increased by 1 is 64', it can be intriguing to explore different approaches to arrive at the answer. Let's break down this problem using various methods and highlight the algebraic solution that most accurately represents the problem statement.

Introduction to the Problem

The problem involves finding a number that, when tripled and increased by 1, equals 64. This can be expressed mathematically as:

3x 1 64

Solving the Problem Step-by-Step

Method 1: Step-by-Step Arithmetic and Algebraic Solution

The first step in solving the problem requires us to isolate the variable x. We start by setting the equation as:

3x 1 64

Subtract 1 from both sides of the equation:

3x 63

Next, divide both sides by 3 to solve for x:

x 63 / 3

x 21

The number we are looking for is 21.

Verification

To verify, we substitute the value of x back into the original equation:

3(21) 1 63 1 64

This confirms that our solution is correct.

Exploring Ambiguity in Problem Statements

Alternative Interpretations

While the above method is the straightforward and expected interpretation of the problem, it is worth noting that the problem statement can be ambiguous. For example, did the question actually mean:

“Thrice the number, increased by 1, is 64” (as we solved above) “Thrice a number, and then increase the result by 1, is 64” (which would mean (3x) 1 64) “A number, when increased by 1, thence tripled, is 64” (which would mean x 1 64 / 3) “A number, when thrice increased and then increased again, is 64” (which would mean (3x) (x 1) 64)

Each of these interpretations would lead to a different equation and a different solution. However, the problem as stated most likely points to the first and third interpretations.

Conclusion

The correct and most straightforward solution to the problem "thrice a number increased by 1 is 64" is x 21. This solution aligns with the standard interpretation of the problem and demonstrates the application of basic algebraic techniques to solve linear equations.

Additional Resources

If you're interested in learning more about solving algebraic equations or need help with similar problems, consider exploring online resources such as Khan Academy, , or other educational platforms. These resources offer step-by-step guides and practice exercises to help you improve your problem-solving skills.