Mr. Mathemagician asks you to pick any whole number. Add 10. Multiply the result
by 4. Add 200. Divide by 4. Subtract your original number. Mr. Mathemagician says,
“You’re final result is 60!” Explain Mr. Mathemagician’s trick?
x =original number
Mathematical operations:
Add 10 :
x + 10
Multiply the result by 4 :
( x + 10 ) * 4
Add 200 :
( x + 10 ) * 4 + 200
Divide by 4 :
[ ( x + 10 ) * 4 + 200 ] / 4
Subtract your original number :
[ ( ( x + 10 ) * 4 + 200 ) / 4] - x
Equation is:
[ ( ( x + 10 ) * 4 + 200 ) / 4 ) ] - x =
= ( x + 10 ) * 4 / 4 + 200 / 4 - x =
x + 10 + 50 - x = 60
Well, Mr. Mathemagician sure knows how to play with numbers! Let's break down his trick step by step, and hopefully, we won't get too lost along the way.
So, let's say you picked the number 'x.'
1. Add 10 to your original number: x + 10
2. Multiply the result by 4: 4(x + 10)
3. Add 200: 4(x + 10) + 200
4. Divide by 4: (4(x + 10) + 200)/4
5. Subtract your original number: (4(x + 10) + 200)/4 - x
Now, let's simplify this equation and find out what our final result really is.
First, let's distribute the 4 to the terms inside the brackets:
(4 * x) + (4 * 10) + 200
That simplifies to:
4x + 40 + 200
Combining like terms, we get:
4x + 240
Now, let's divide this whole expression by 4:
(4x + 240)/4
That simplifies to:
x + 60
And this is where the trickery lies! Mr. Mathemagician claims that the final result is 60. But in reality, the expression x + 60 equals the original number you picked!
So, no matter what whole number you choose at the beginning, the final result will always be the number you started with. It's a sneaky way of making you think there was some magical transformation, but it's just a fancy mathematical flimflam!
And there you have it, Mr. Mathemagician's clever trick revealed!
Mr. Mathemagician's trick involves a series of mathematical operations that will always result in the number 60, regardless of the original number chosen.
Step 1: Pick any whole number.
Let's say the original number chosen is represented by the variable "x".
Step 2: Add 10.
Adding 10 to the original number (x) gives us x + 10.
Step 3: Multiply the result by 4.
Multiplying (x + 10) by 4 gives us 4(x + 10) = 4x + 40.
Step 4: Add 200.
Adding 200 to the previous result (4x + 40) gives us (4x + 40) + 200 = 4x + 240.
Step 5: Divide by 4.
Dividing the result by 4 gives us (4x + 240) / 4 = x + 60.
Step 6: Subtract your original number.
Subtracting the original number (x) from the previous result (x + 60) gives us (x + 60) - x = 60.
Therefore, no matter what number is chosen initially, the final result of the trick will always be 60.
Mr. Mathemagician's trick is based on a clever mathematical manipulation using a series of operations. Let's break it down step by step:
1. Pick any whole number: Let's call this number "x."
2. Add 10: You now have x + 10.
3. Multiply the result by 4: This gives you 4(x + 10).
4. Add 200: The expression becomes 4(x + 10) + 200.
5. Divide by 4: Now we have (4(x + 10) + 200)/4.
6. Subtract your original number: Subtracting "x" from the previous result, we get (4(x + 10) + 200)/4 - x.
Now, let's simplify the expression:
Distributing the 4 inside the parentheses:
(4x + 40 + 200)/4 - x
Combining like terms:
(4x + 240)/4 - x
Simplifying:
x + 60 - x
The "x" terms cancel each other out, leaving us with 60. Therefore, Mr. Mathemagician's trick always leads to the final result of 60, regardless of the original number chosen.
In other words, no matter which number you pick at the start, the series of operations simplifies to 60. It is a mathematical trick designed to give the appearance of a magical prediction.