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Math Help - Can you turn this into an Algebraic Explanation?

  1. #1
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    Can you turn this into an Algebraic Explanation?

    I don't know if this is considered advanced/uni math so sorry in advance if this is in the wrong section, but here's my problem:

    There is a trick that I found over the internet and I was given the challenge of making it into an Algebraic Explanation.

    Here's the trick

    1: Grab a calculator (You wont be able to do this one in your head) .
    2: Key in the first three digits of your phone number (NOT the area code-if your number is 01-123-4567, the 1st 3 digits are 123).
    3: Multiply by 80.
    4: Add 1.
    5: Multiply by 250.
    6: Add the last 3 digits of your phone number with a 0 at the end as one number eg, 5670
    7: Repeat step 6
    8: Subtract 250
    9: Divide number by 20

    I was given
    the number you start with, 123 or whatever, can be thought of as 100x1 + 10x2 + 3
    as a hint.

    I've tried playing around with it, giving the numbers variables etc but I still can't turn it into an explanation - I don't even know how to turn it into an explanation.

    Thanks in advance
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  2. #2
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    skeeter's Avatar
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    Re: Can you turn this into an Algebraic Explanation?

    let a = 1st digit, b 2nd digit , c 3rd digit

    100a + 10b + c

    Multiply by 80 ...

    8000a + 800b + 80c

    Add 1 ...

    8000a + 800b + 80c + 1

    Multiply by 250 ...

    2000000a + 200000b + 20000c + 250

    Add the last 3 digits of your phone number with a 0 at the end as one number eg, 5670

    let d = 1st digit, e 2nd digit , f 3rd digit

    2000000a + 200000b + 20000c + 1000d + 100e + 10f + 250

    Repeat step 6 ...

    2000000a + 200000b + 20000c + 2000d + 200e + 20f + 250

    Subtract 250 ...

    2000000a + 200000b + 20000c + 2000d + 200e + 20f

    Divide number by 20 ...

    you finish it.
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