Math Challenge!?

Question

This is a neat little trick that will always give you the last 7 digits of your phone number always! So grab your calculators!

1. Key in the first three digits of your phone number. (No area code.)
2. Multiply by 80
3. Add 1
4. Multiply by 250
5. Add the last 4 digits of your phone number.
6. Add the last 4 digits of your phone number again.
7. Subtract 250.
8. Divide by 2.

Pretty cool, huh?
Explain to me algebraically how this works.

Answer 1

1. Let x, y, and z be the first three digits of the number.
2. 80xyz
3. 80xyz + 1
4. 250(80xyz + 1)
5. Let a, b, c, and d be the last four digits of the number.
250(80xyz + 1) + abcd
6. 250(80xyz + 1) + 2abcd
7. 250(80xyz + 1) + 2abcd – 250 =
250(80xyz) + 2abcd
8. (250(80xyz) + 2abcd)/2
250(40xyz) + abcd
10,000xyz + abcd

All this does is shift the first three digits into the proper places in a base-10 positional notation, leaving the last four in their proper, respective positions.

Answer 2

Say the digits of your phone number, in order, are a, b, c, d, e, f, g.
If you concatenate them, they form a seven-digit number that is equivalent to:
10⁶a+10⁵b+10⁴c+10³d+10²e+10f+g

Your trick goes through a bunch of steps to create this number.

Answer 3

100h+10t+u [1st three digits of phone number]
8000h + 800t +80u [times 80]
8000h +800t +80u +1 [ add 1]
2000000h + 200000t + 20000u + 250 [ times 250]
2000m + 200h1+20t1 + 2u1 [last 4 digits * 2]
2000000h+200000t +20000u +2000m +200h1+20t1+2u1
1000000h+100000t +10000u +1000m +100h1+10t1+u1
This gives your 7digit phone number

Answer 4

thats amazing!

Answer 5

that is wicked sweet!! sry, i dunno how though...

Answer 6

wow it works but idk how it works.