Math Geniuses!! Please help me with this Problem of the Week...?

Question

Math Geniuses!! Please help me with this Problem of the Week...?
Math Geniuses!! Please help me with this Problem of the Week...?
I'd be passing Trig if i get this one! So please help me out as much as you can, and i'll love you forever :)
WARNING: THIS IS SUPER HARD. NO ONE CAN FIGURE IT OUT IN MY CLASS (and i have a smart class)

IF a 2-digit integer is "k" times the sum of its digits, then the number formed by reversing the digits of the original number is the sum of its digits multiplied by what number (in terms of "k")?

This is confusing i have no idea what they're talking about.

Thanks guys!!! Even if you dont get it, i give you credit for trying!!!

Answer 1

In your problem you state "multiplied by what number (in terms of "k")"
Let a = "what number"

Given a 2-digit integer,
Let x = the tens digit
Let y = the ones digit and where

k = (10x +y) / (x + y)

Solution (but you'll have to figure how I got to this!)

k ( 10y + x )
--------------- = a
( 10x + y )

Try a number where N = the 2 digit number
N = 43 (x = 4, y = 3)

k = 43/(4+3) = 6.142857...

6.142857... * (10 * 3 + 4)
------------------------------ = a = 4.857143...
(10 * 4 + 3)

a * (4 + 3) = 34 <-- digits reversed from 43

Note: The answer given in the next answer is faulty in that the goal is to find the Reversed 2-digit integer. He uses the Reversed 2-digit integer in the solution. In other words, he's using the answer to find the answer.

Answer 2

...I thought this one would take me a while...but after checking my answers four times, I believe I have found what your teacher is looking for.

The answer is:

Reversed 2-digit integer
___________________ K

Original 2-digit integer


In other words: (Reversed 2-digit integer / Original 2-digit integer)K

This works for every number that I have tried. If you need more explanation, maybe this example will help. The number that is the answer will be represented by x:

2-digit integer:71

8k=71

k=71/8
----------

8xk=17

xk=17/8

x(71/8)=17/8

x=(17/8)/(71/8)

x=17/71

x=(reversed 2 digits)/(original 2 digits)

I know it's confusing but this is the correct answer (just remember to keep it in terms of K.

Answer 3

k and 27 k times 9 ,,,then 72 then k times 9=72 k=8 maybe the question is kind of worded weird, or maybe do that backwards and the original number is 72, not sure

Answer 4

Oh wow......I thought I was a math geneous until I saw that. I get the first little part but then after that I am stumped.

Answer 5

The answer is "k"