SOLUTION: the sum of the digits of a three-digit number is 16. the second digit in the number is three times the third digit. the three-digit number obtained by reversing the order of the di
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Question 675650: the sum of the digits of a three-digit number is 16. the second digit in the number is three times the third digit. the three-digit number obtained by reversing the order of the digits is 594 less than the original number. find the three digits?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum of the digits of a three-digit number is 16. the second digit in the number is three times the third digit. the three-digit number obtained by reversing the order of the digits is 594 less than the original number. find the three digits?
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Original Number: 100h + 10t + u
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Equations:
h + t + u = 16
t = 3u
100u + 10t + h = 100h + 10t + u - 594
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Modify the 3rd equation:
h + t + u = 16
t = 3u
99u - 99h = -594
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Substitute for "t" so you have only 2 variables:
Divide thru the bottom equation by 99:
h + 4u = 16
-h + u = -6
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Add to get:
5u = 10
u = 2
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Then t = 3u = 6
And h + 6 + 2 = 16
So h = 8
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Original Number: 862
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Cheers,
Stan H.
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