SOLUTION: The digits of a two digit number sum to 10. If the digits swap places the number is 36 more than the original number. What is the original number? Can you show an algebraic soluti

Algebra ->  Equations -> SOLUTION: The digits of a two digit number sum to 10. If the digits swap places the number is 36 more than the original number. What is the original number? Can you show an algebraic soluti      Log On


   

Question 859766: The digits of a two digit number sum to 10. If the digits swap places the number is 36 more
than the original number. What is the original number? Can you show an algebraic solution?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
The digits of a two digit number sum to 10. If the digits swap places the number is 36 more
than the original number. What is the original number? Can you show an algebraic solution?
t = the tens digit
u = the units (or ones) digit
10t+u = the original number
10u+t = the number with digits t and u swapped

The digits of a two digit number sum to 10. 

%22%22%2B%22%22%22%22=%22%2210

t + u = 10


If the digits swap places the number is 36 more than the original number.

%22%22=%22%22%28matrix%286%2C1%2CThe%2C+original%2C%22number%2C%22%2Cwhich%2C+is%2C+%2810t%2Bu%29+%29%29%22%22%2B%22%22%28matrix%282%2C1%2C%0D%0A%0D%0A36%2Cmore%29%29              


(10u+t) = (10t+u) + 36

So solve the system of two equations and two unknowns:

system%28t+%2B+u+=+10%2C+%2810u%2Bt%29+=+%2810t%2Bu%29+%2B+36%29

Get t = 3 and u = 7, So the original number is 37.

Edwin