Solving a Marbles Riddle and Its SEO Optimization for Google

SEO optimization is crucial for content to rank well on Google. In this article, we will dissect a math puzzle related to marbles and solve it using algebraic equations. We will then discuss how to optimize the content for better visibility and engagement on Google.

Introduction to the Puzzle

Jose had a bag of marbles. 3/5 of the marbles were blue, and 1/4 of the remainder were green. If there are 40 more blue marbles than green marbles, how many marbles did Jose have in total?

Solution to the Puzzle

We can solve this problem using algebraic equations. Let the total number of marbles be represented by x.

Step 1: Calculate the Number of Blue Marbles

The number of blue marbles is 3/5 of the total:

[ text{Number of blue marbles} frac{3}{5}x ]

Step 2: Calculate the Remainder of the Marbles After Removing the Blue Ones

The remainder is the total number of marbles minus the blue marbles:

[ text{Remainder} x - frac{3}{5}x frac{2}{5}x ]

Step 3: Calculate the Number of Green Marbles

The green marbles are 1/4 of the remainder:

[ text{Number of green marbles} frac{1}{4} times frac{2}{5}x frac{1}{10}x ]

Step 4: Set Up the Equation Based on the Given Condition

There are 40 more blue marbles than green marbles:

[ frac{3}{5}x frac{1}{10}x 40 ]

Step 5: Solve the Equation

Let's solve the equation step by step. First, clear the fractions by multiplying the entire equation by 10:

[ 10 cdot frac{3}{5}x 10 cdot frac{1}{10}x 10 cdot 40 ]

This simplifies to:

[ 6x x 400 ]

Rearrange the equation to isolate x:

[ 6x - x 400 ]

Simplify:

[ 5x 400 ]

Divide both sides by 5:

[ x 80 ]

Conclusion

José had a total of 80 marbles.

Verification

Number of blue marbles: (frac{3}{5} times 80 48) Remainder: (80 - 48 32) Number of green marbles: (frac{1}{4} times 32 8) Check: 48 blue marbles are indeed 40 more than 8 green marbles.

Final Answer: 80 marbles.

SEO Optimization for Google

To optimize the content for Google, you should include the following elements:

Title Tag: Use the primary keyword in the title e.g., "Solving a Marbles Puzzle - Algebraic Equations and SEO Tips". Meta Description: Include a meta description that captures the essence of the content and includes the primary keyword. For example: "Learn how to solve a marbles riddle using algebraic equations and understand the importance of SEO for online visibility." Heading Tags (H2, H3): Use heading tags to structure the content. Headings make the content easier to read and follow, which is crucial for user satisfaction and SEO. Use descriptive and relevant headings with the primary and secondary keywords. Internal Links: Include internal links to related content like other math puzzles or SEO optimization guides, as this encourages users to explore more of your site. Image Alt Text: Use descriptive alt text for any images included in the article. This not only helps Google understand the content better but also provides a better user experience. Use primary and secondary keywords in the alt text.

By following these SEO best practices, you can optimize your content for better visibility and engagement on Google.

Keywords: math puzzle, algebraic equation, Google SEO optimization