How does this work “Think of a #. Add 7. Double the result. Subtract 8. Double the result. Add 12. Divide by 4. Subtract 6. Your answer will be the original number.
Think of a #. ---- x
Add 7 ---- x+7
Double the result ----- 2x+14
subract 8 ---- 2x+6
double the result ---- 4x+12
add 12 ------ 4x + 24
divide by 4 ---- x + 6
subtract 6 ---- x
Mathemagics!
The provided process is a mathematical trick that works consistently due to the operations involved. Here's an explanation of how it works using algebraic notation:
1. "Think of a #": Let's represent the original number as 'x'.
2. "Add 7": Adding 7 to 'x' gives us 'x + 7'.
3. "Double the result": Multiplying 'x + 7' by 2 gives us '2(x + 7)'.
4. "Subtract 8": Subtracting 8 from '2(x + 7)' gives us '2(x + 7) - 8'.
5. "Double the result": Multiplying '2(x + 7) - 8' by 2 gives us '2(2(x + 7) - 8)'.
6. "Add 12": Adding 12 to '2(2(x + 7) - 8)' gives us '2(2(x + 7) - 8) + 12'.
7. "Divide by 4": Dividing '2(2(x + 7) - 8) + 12' by 4 gives us '1/4[2(2(x + 7) - 8) + 12]'.
8. "Subtract 6": Subtracting 6 from '1/4[2(2(x + 7) - 8) + 12]' gives us '1/4[2(2(x + 7) - 8) + 12] - 6'.
By simplifying the expression further, we have:
1/4[2(2(x + 7) - 8) + 12] - 6
= 1/4[2(2x + 14 - 8) + 12] - 6
= 1/4[2(2x + 6) + 12] - 6
= 1/4[4x + 12 + 12] - 6
= 1/4[4x + 24] - 6
= 1/4 * 4(x + 6) - 6
= (x + 6) - 6
= x
So, no matter what number 'x' you start with, following the provided process will eventually bring you back to your original number.