# Thread: Can you turn this into an Algebraic Explanation?

1. ## 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.
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.

2. ## 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

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.