SOLUTION: The product of the digits of a positive two-digit number exceeds the sum of the digits by 39. If the order of the digits is reversed, the number is increased by 27. Find the number

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Question 747280: The product of the digits of a positive two-digit number exceeds the sum of the digits by 39. If the order of the digits is reversed, the number is increased by 27. Find the number.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Two digit number, x for the tens, y for the units. This number is like 10*x+y.
product: xy
sum of the digits: x+y
the reversal of the digits: 10y+x is the number.

product of the digits of a positive two-digit number exceeds the sum of the digits by 39, means:
xy=x%2By%2B39

the order of the digits is reversed, the number is increased by 27, means:
10y%2Bx=10x%2By%2B27

System of Equations is:
highlight%28xy=x%2By%2B39%29
highlight%2810y%2Bx=10x%2By%2B27%29
The second equation simplifies to ....
9y=9x%2B27 further becomes--------
y=x%2B3, so solve this equation for either x or y, and substitute this into the first equation, and solve for the other variable. Now use either equation to solve for the first variable.