SOLUTION: if a number is divided by 72 it leaves 71 as remainder. The same number divided by 81 leaves 80 as remainder find the number

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Question 810486: if a number is divided by 72 it leaves 71 as remainder. The same number divided by 81 leaves 80 as remainder find the number
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x/72=y+71/72,
x/81=z+80/81
72=9*8
81=9*9
x=1295
1295/72=17 71/72
1295/81=15 80/81


Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
if a number is divided by 72 it leaves 71 as remainder. The same number divided by 81 leaves 80 as remainder

        QUOTIENT
DIVISOR)DIVIDEND
        
         REMAINDER
             
        
In a division, if the remainder is 1 less than the divisor,
then the dividend must have been 1 less than a multiple of 
the divisor, like this:
        
       3
    7)27
      21
       6

Here the remainder is 6, 1 less than the divisor 7, because
the 27 is 1 less than 28, a multiple of 7

That's true in both these cases.  So 1 less than any common
multiple of 72 and 80 must be a solution.

The least common multiple of 72 and 81 is 648, so the smallest
answer is 648-1 or 647.

However there are infinitely many answers.  The next common
multiple of 72 and 80 is 1296, so 1295 is also a solution, etc., etc.

Edwin