Solving for the Mystery Number: A Mathematical Puzzle

Imagine a mathematical puzzle that demands your attention. We have a mystery number, and with just a bit of algebra, we can unveil its identity. This article will guide you through the process of solving a seemingly complex problem, breaking it down step by step.

The Puzzle: Breakdown and Solution

We are given a problem stating that if we divide a mystery number by 9 and then subtract 7, the result is 1. Denote this mystery number as x. The equation can be set up as follows:

frac{x}{9} - 7 1

Let's solve for x step by step:

Add 7 to both sides of the equation to isolate the division term:
(frac{x}{9} 1 7)

(frac{x}{9} 8)

Multiply both sides by 9 to solve for x:
(x 8 times 9)

(x 72)

Here’s the step-by-step proof to verify the solution:

Divide 72 by 9: (72 div 9 8) Subtract 7 from the result: (8 - 7 1) As a result, the mystery number is 72.

Reverse Engineering the Solution

The reverse engineering approach can also be utilized to solve the same problem. It involves un-doing the operations step by step as they were applied to the unknown number x.

Add 7 to 1 to reverse the subtraction step:

(1 7 8)

Multiply 8 by 9 to reverse the division step:

(8 times 9 72)

Additional Examples

Example 1:

What if the equation was: (x div 8 - 7 1)

(x div 8 1 7)

(x div 8 8)

(x 8 times 8)

(x 64)

The mystery number in this case is 64.

Example 2:

Consider the problem: What's the number that, when divided by 9 and then subtracting 7, results in 1?

The number is 72, as derived by the steps above.

Conclusion

Through these examples, we’ve seen that solving for the mystery number involves basic algebraic operations. The key is to understand the order of operations and reverse them to find the unknown value. Whether you're a math enthusiast or a student looking to refine your skills, understanding this process can be incredibly enlightening.