A three-digit number has two properties
belongs to book: A First Course in Linear Algebra|Robert A. Beezer|| Chapter number:1| Question number:C50
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total answers (1)
belongs to book: A First Course in Linear Algebra|Robert A. Beezer|| Chapter number:1| Question number:C50
total answers (1)
Let a be the hundreds digit, b the tens digit, and c the ones digit. Then the first condition says that b + c = 5.
need an explanation for this answer? contact us directly to get an explanation for this answerThe original number is 100a + 10b + c, while the reversed number is 100c + 10b + a. So the second condition is
792 = (100a + 10b + c) - (100c + 10b + a) = 99a - 99c
So we arrive at the system of equations
b + c = 5
99a - 99c = 792
Using equation operations, we arrive at the equivalent system
a - c = 8
b + c = 5
We can vary c and obtain infinitely many solutions. However, c must be a digit, restricting us to ten values (0 -
9). Furthermore, if c > 1, then the first equation forces a > 9, an impossibility. Setting c = 0, yields 850 as a
solution, and setting c = 1 yields 941 as another solution.