Unraveling the Mystery of X: An Engaging Algebra Puzzle
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Chapter 1: Introduction to the Puzzle
The wealth gap between me and a billionaire may average out to half a billion dollars. But does this statistic hold any real value?
Are you able to apply the average formula to determine the elusive value of x?
Take a moment to pause this reading, grab a pen and paper, and tackle the problem yourself. Once you’re set, continue for the solution!
Video Description: In this geometry challenge, you'll need to determine angle X. Test your skills and see if you can solve this engaging puzzle!
Solution
To find the average of 1 and 2, simply add them together and divide by the number of values, which is 2.
Thus, (1 + 2) / 2 = 1.5.
Applying this method to our problem leads us to the following calculation:
We divide by 100 because we have a total of 99 terms from 1 to 99, plus the additional term of x.
The sum of integers from 1 to 99 can be calculated using the formula n(n + 1) / 2, where n represents the last number in this sequence.
In this case, 99 + 1 gives us 100, and dividing this by 2 results in 50.
Hopefully, you’re following along with the algebra thus far.
The next step is to isolate x.
You would multiply both sides of the equation by 100 and then rearrange the equation to get all instances of x on one side.
A helpful observation here is recognizing that 9999 can be expressed as 99 × 101.
This allows us to cancel the 99s on both sides, simplifying our equation to:
And there you have it—the solution!
How incredible is that?
What thoughts crossed your mind while solving this puzzle? I’d love to hear your insights in the comments!
Chapter 2: Explore More Puzzles
Video Description: Learn the techniques for finding the value of x in various algebraic contexts. Perfect for sharpening your math skills!
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Happy Solving,
Bella
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