The Mystery of the Missing X

 The Mystery of the Missing X

Alice was a curious girl who loved to solve puzzles and mysteries. She had a knack for finding clues and figuring out solutions. She also loved math, especially algebra. She enjoyed playing with numbers and symbols, and finding the value of unknowns.

One day, she received a letter from her friend Bob, who lived in another town. He wrote:

"Dear Alice,
I need your help. Something terrible has happened. Someone has stolen my X!
X is my pet parrot, who can talk and sing and do math. He is very smart and friendly, and I love him very much.

He was kidnapped last night, when I was asleep. The thief left a note on his cage, with a riddle. It says:

If you want to see your X again, solve this equation:

                    3x + 2 = 35 

The answer is the number of the house where I am hiding your X.

But be careful, there is a twist.
The house number is written in Base 5, not Base 10.
You have to convert it to Base 10 before you can find it.
Hurry up, or you will never hear him speak again!

Signed,
The Algebra Bandit'

Alice, please help me find my X. He is the only friend I have in this town. I don't know how to solve the equation, or how to convert bases. And I don't have much time.

Please reply soon.

Your friend,
  Bob"

Alice was shocked and angry. How could someone be so cruel and mean? She felt sorry for Bob and his X. She decided to help him right away. She took out her notebook and pen, and wrote back:

"Dear Bob, Don't worry. I will help you find your X. I know how to solve the equation and convert bases.

The equation is:

                 3x + 2 = 35 

To solve it, we need to find the value of x that makes the equation true.

To do that, we need to isolate x on one side of the equation, and move everything else to the other side.

We can do that by using some rules of algebra, such as:

- We can add or subtract the same number from both sides of the equation, without changing its meaning.

- We can multiply or divide both sides of the equation by the same number (except zero), without changing its meaning.

Let's start by subtracting 2 from both sides of the equation. 

Simplifying, we get:

Now, we need to get rid of the 3 that is multiplying x. We can do that by dividing both sides of the equation by 3. This will cancel out the 3 on the left side, and leave us with:

Simplifying, we get:                                        

We have found the value of x that makes the equation true. It is 11.

But this is not the end of the puzzle. The Algebra Bandit said that the house number is written in base 5, not base 10. To find the correct house number, we need to convert 11 from Base 5 to Base 10.

Base 5 is a different way of writing numbers, using only digits from 0 to 4. 

Base 10 is the usual way of writing numbers, using digits from 0 to 9.

To convert a number from Base 5 to Base 10, we need to use this formula:

(base 5 number) = (digit in ones place) * (5^0) + (digit in fives place) * (5^1) + (digit in twenty-fives place) * (5^2) + ...

For example, to convert 23 from Base 5 to Base 10 , we do this:

                   

To convert 11 from Base 5 to Base 10:

This means that the number of the house where the Algebra Bandit is hiding your X is **11** in Base 5, or **6** in Base 10.

Go to that house and rescue your X. Be careful, though. The Algebra Bandit might be dangerous.

Good luck!

Your friend,

  Alice".

Alice folded the letter and put it in an envelope. She ran to the post office and mailed it to Bob.

She hoped that he would receive it soon, and that he would find his X safe and sound.

She also hoped that the Algebra Bandit would be caught and punished for his crime.

She wondered who he was, and why he did what he did.

She wondered if there were more equations and bases to solve, and more mysteries to unravel.

She smiled and thought to herself:

"I love algebra!".