Solving a Mathematical Puzzle: Finding Consecutive Multiples of 5 that Sum to 75

Mathematics is a fascinating field where problems can be both challenging and fulfilling. One such intriguing puzzle revolves around finding a series of consecutive multiples of 5 that add up to 75. Let's explore how to solve this puzzle step by step.

The Problem

Given that the sum of three consecutive multiples of 5 is 75, we are tasked with identifying the first number in this series. To resolve this, we can follow these logical steps:

Step 1: Write Out Consecutive Multiples of 5

Let the first number be represented by x. The next two consecutive multiples of 5 can be denoted as x 5 and x 10.

Step 2: Set Up the Equation

The sum of these three consecutive multiples is given by:

x x 5 x 10 75

Combining like terms, we get:

3x 15 75

Step 3: Solve for x

Subtract 15 from both sides of the equation:

3x 60

Then, divide both sides by 3:

x 20

Step 4: Confirm the Solution

Substitute x 20 back into the consecutive multiples:

Adding these values together:

20 25 30 75

This confirms that our solution is correct.

Interpreting the Solution

The solution to the puzzle is that the consecutive multiples of 5 that sum to 75 are 20, 25, and 30. These numbers form a logical and consistent sequence based on the rules of the problem.

Conclusion

This puzzle not only tests basic arithmetic skills but also reinforces the importance of logical reasoning and systematic problem-solving. Whether you are a math enthusiast, a student, or simply someone who enjoys mental challenges, understanding such mathematical puzzles can provide valuable cognitive benefits.

Exploring these kinds of mathematical problems teaches us to break down complex issues into simpler components, and from there, to find a clear and logical path to the solution. Whether you need to brush up on your algebra skills or just enjoy the satisfaction of solving a mathematical challenge, this puzzle offers both valuable learning and entertainment.