SOLUTION: The difference between a 2- digit number and the number obtained by interchanging its digits is 27. What is the difference between the sum and the difference of the digits of the n

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Question 896327: The difference between a 2- digit number and the number obtained by interchanging its digits is 27. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1:2 ?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between a 2- digit number and the number obtained by interchanging its digits is 27. 
%2810t%2Bu%29-%2810u%2Bt%29+=+27
10t%2Bu-10u-t+=+27
9t-9u+=+27
t-u+=+3

This tells us that t is larger than u, which we'll need
to know for the next part:

...the ratio between the digits of the number is 1:2 ?

Since t is larger than u we know that this means

u%2Ft=1%2F2 and not cross%28t%2Fu=1%2F2%29


u%2Ft=1%2F2
2u=t

So we have the system of two equations:

system%28t-u=3%2C2u=t%29

Solve by substituting:

t-u=3
2u-u=3
u=3

2u=t
2%283%29=t
6=t

So the number is 63.

Edwin