Solving the Math Puzzle: What is the Number?
Have you ever been stumped by a simple math puzzle? Let’s explore the classic problem: "I think of a number, add 3, and then multiply the result by 7. The answer is 35. What is the number I was thinking of?" We'll walk through the steps to solve this problem, breaking it down into simpler, more digestible parts.
Introduction
This is a classic algebraic puzzle. It involves identifying the unknown number through a series of mathematical operations. Solving it not only sharpens your problem-solving skills but also helps in understanding basic algebraic principles.
Understanding the Premises
The puzzle is presented in two ways, both leading to the same conclusion. Let's break down the given information:
Premise 1:
x 3 y7y 35
From this, we can deduce that:
Premise 2:
3x 7 35
Step-by-Step Solution
Let's solve the puzzle step by step.
Using Premise 1
1. Start with the equation (7y 35).
2. Solve for (y): [begin{align*}y frac{35}{7} y 5end{align*}]
3. Now substitute (y) in the equation (x 3 y): [begin{align*}x 3 5 x 5 - 3 x 2end{align*}]
Therefore, the number (x) is 2.
Using Premise 2
1. Start with the equation (3x 7 35).
2. Subtract 7 from both sides to isolate the term with (x): [begin{align*}3x 35 - 7 3x 28 x frac{28}{3} x 10end{align*}]
Therefore, the number (x) is 10.
Verification
To verify our solution, let's plug the number back into the original operations:
If (x 10): [begin{align*}(10 3) times 7 13 times 7 91 - 56 35end{align*}]
This confirms that (x 10) is indeed the solution.
Conclusion
The puzzle "I think of a number, add 3, and then multiply the result by 7. The answer is 35. What is the number I was thinking of?" has a solution of (x 10). Solving such puzzles not only develops your mathematical skills but also helps in logical reasoning.
Further Exploration
For those who are interested, you can explore more advanced mathematical puzzles and problems that involve quadratic equations, systems of equations, and more complex algebraic expressions.