Is there a Percent where when written forward plus backward equal 100?
Example:
XY + YX = 100
(where those variables aren't multiplied together but stand in for the 10s-digit (X) + digit (Y) = 10s-digit (Y) + Digit (X)
I came up with this question bc I saw some ground meat that had a 73% Meat + 27% Fat Ratio. Of course 73+27 does equal 100 because neither 73 nor 27 are palindrome of each other.
So, is there any palindrome that when added together equal 100? I don't think there is a solution, but like I said I'm no math genius!
And if so, how would it be written out first as a problem, and the proved by solving it? I'd love to see your work in figuring this out. I'm by no means a Mathematician, so I have no idea how to write this out except in the example above.
This has nothing to do with school or anything, I just became curious when I saw the very similar numbers on my package of ground beef.
I think the actual equation would look like this, but I could be completely wrong:
(10X+Y) + (10Y+X) = 100
Is there any solution? How's it actually written and afterward how is it solved and proven?
Thanks a lot!
$$(10X+Y) + (10Y+X) = 100\\11X+11Y = 100\\11(X+Y) = 100$$ The left hand side is a multiple of 11, but the right hand side is not. There is therefore no solution.
By the way, a palindrome is a number/word/sentence that reads the same backwards as forwards, so that is not the right term for these reversed pairs of numbers.