Can someone explain how this works?

Question

1. Key in the first three digits of your phone number (NOT the Area code...)
2. Multiply by 80
3. Add 1
4. Multiply by 250
5. Add to this the last 4 digits of your phone number
6. Add to this the last 4 digits of your phone number again.
7. Subtract 250
8. Divide number by 2

Do you recognize the answer??

Answer 1

Let number = 1234567
x = 123
y = 4567
Number = 1000x + y

Following each step
x
80x
80x + 1
250(80x + 1) = 20000x + 250
20000x + 250 + y
20000x + 250 + 2y
20000x + 2y
10000x + y

As x was the 1st 3 digits, 10000x + y gives the original phone number.

Answer 2

Your number is xxxyyyy

1. xxx
2. 80 * xxx
3. 80 * xxx  + 1
4. 20000 * xxx + 250
5. 20000 * xxx + 250 + yyy
6. 20000 * xxx + 250 + 2 * yyyy
7. 20000 * xxx + 250 + 2 * yyyy - 250
   20000 * xxx + 2 * yyyy
8. 10000 * xxx + yyyy

Result is xxxyyyy

Answer 3

Here are the instructions again:

1. Key in the first three digits of your phone number (NOT the Area code...)
2. Multiply by 80
3. Add 1
4. Multiply by 250
5. Add to this the last 4 digits of your phone number
6. Add to this the last 4 digits of your phone number again.
7. Subtract 250
8. Divide number by 2

Let your phone number be "ABC-DEFG".

Let x be the number we have so far.

1. x = 100*A + 10*B + C
2. x = 8000*A + 800*B + 80*C
3. x = 8000*A + 800*B + 80*C + 1
4. x = 2000000*A + 200000*B + 20000*C + 250
5. x = 2000000*A + 200000*B + 20000*C + 250 + 1000*D + 100*E + 10*F + G
6. x = 2000000*A + 200000*B + 20000*C + 250 + 2000*D + 200*E + 20*F + 2*G
7. x = 2000000*A + 200000*B + 20000*C + 2000*D + 200*E + 20*F + 2*G
8. x = 1000000*A + 100000*B + 10000*C + 1000*D + 100*E + 10*F + G

Thus, we get back "ABC-DEFG".