Solving the Marble Puzzle: A Step-by-Step Guide for SEO Optimization

Have you ever come across a puzzle that requires a bit of algebra to solve? Today, we're going to tackle a classic marble problem that might have appeared in a math textbook or on your homework. Let's dive in and solve it together while discussing SEO optimization tips!

The Puzzle: Solving for Blue Marbles

The puzzle goes as follows: Keith had 694 green, yellow, and blue marbles altogether. He had three times as many blue marbles as yellow marbles. There were 90 fewer green marbles than blue marbles. How many blue marbles did Keith have?

Breaking Down the Problem

This puzzle consists of a simple set of linear equations. Let's define our variables:

G Number of green marbles Y Number of yellow marbles B Number of blue marbles

Here are the relationships described in the puzzle:

The total number of marbles is 694: G Y B 694. Keith has three times as many blue marbles as yellow marbles: 3Y B. There are 90 fewer green marbles than blue marbles: G B - 90.

Solving the Equations

With these equations, we can solve for the number of blue marbles. Let's start by substituting the second and third equations into the first:

From the second equation, we get:

B 3Y.

From the third equation, we get:

G B - 90 3Y - 90.

Now, substituting these into the first equation:

(3Y - 90) Y 3Y 694.

Simplifying this, we get:

7Y - 90 694.

Adding 90 to both sides gives us:

7Y 784.

Dividing both sides by 7, we get:

Y 112.

Now, using B 3Y:

B 3 * 112 336.

So, Keith had 336 blue marbles.

Verifying the Solution

Let's verify our solution:

Green marbles: G B - 90 336 - 90 246. Yellow marbles: Y 112. Blue marbles: B 336. Total marbles: G Y B 246 112 336 694.

All the conditions are satisfied, confirming our solution.

SEO Optimization Tips for Mathematics Content

When optimizing content for search engines, especially mathematical content, here are a few tips to consider:

Use Descriptive Titles: Use titles that clearly describe the content, such as “Solving the Marble Puzzle: A Step-by-Step Guide”. Add H1 and H2 Tags: Use heading tags to structure your content and make it more readable. For instance, we used H1 for the main title, H2 for problem statements, and H3 for individual sections. Incorporate Keywords: Use relevant keywords naturally in your content. For example, "algebra puzzles", "marble problems", and "homework help" are keywords that are relevant to this topic. Use Bullet Points and Lists: Break down complex problems and solutions into bullet points or lists for easier readability and quick understanding. Include Visuals: Add images, diagrams, or charts to help illustrate the problem and solution. This can be particularly helpful for mathematics and puzzles.

By following these tips, you can create high-quality, SEO-optimized content that is not only informative but also engaging for your readers.

Conclusion

Mathematics puzzles like the marble problem can be fun and challenging. By breaking them down into a system of equations and solving them step-by-step, we can find the solution efficiently. And by optimizing our content, we can ensure that our solutions reach a broader audience who might be seeking help with similar problems.

Related Keywords

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Remember, always strive to create content that is not just informative but also engaging and optimized for search engines. Happy optimizing!