Why or how does this work?

Question

1. Grab a calculator. (you won't be able to do this one in your head)
2. Key in the first three digits of your phone number (NOT the area code)
3. Multiply by 80
4. Add 1
5. Multiply by 250
6. Add the last 4 digits of your phone number
7. Add the last 4 digits of your phone number again.
8. Subtract 250
9. Divide number by 2
Do you recognize the answer?

Answer 1

take any 3digit number x and four digits y
the "phone number" is x*10000 + y

your formula is
((x*80 + 1)*250 +y +y -250)/2
= x*80*250/2 +2y/2
= x*10000 + y

so it has to work

Answer 2

Let's assign the digits of the phone number to variables.

1st three digits = x and last four digits = y

Now:

.5(250*(80x + 1) + 2y - 250)
.5(20000x + 250 + 2y - 250)
.5(20000x + 2y)
10000x +y

As phone numbers are seven digits, the three digit number creates a number with with those three digits in the millionth, hundred thousandth, and ten thousandth places (in order, as 1*x=x). Therefore, the four digits represented by y go into the thousandth, hundredth, tenth, and ones places (in order, as 0+y=y and there are no digits in those places).

Answer 3

((80x + 1)*250 + 2y -250)/2
=(20000x+250+2y-250)/2
=10000x+125+y-125
=10000x + y

Multiplying x by 10000 yields the three digit x value along with 4 trailing zeros. Adding y replaces those zeros with the last four digits of your phone number.

Answer 4

Let the 1st 3 digits be A, and remember they're in the 10,000's place; let the last 4 be B. So your number is 10,000A + B.

The directions say:
[(80A + 1)250 + 2B - 250] / 2 =
[20,000A + 250 + 2B - 250] / 2 =
[20,000A + 2B] / 2 =
10,000A + B

Answer 5

Let x be the first three digits of my phone number, and y be the rest.

Let d be the value displayed.

2. d=x
3. d=80x
4. d=80x+1
5. d=250(80x + 1) = 20000x + 250
6. d=20000x + 250 + y
7. d=20000x + 250 + 2y
8. d=20000x + 2y
9. d=10000x + y

Answer 6

step 1 -pick a number -
step 2 -double it -
step 3 -add 10 -
step 4 -divide it by 2 -
step 5 -subtract the number you picked in step 1

You get 5

Answer 7

wow thats cool how that works how did you know about this problem