# Math

The sum of digits of a three-digit number is 14, and the ten's digit of the number is one more than the unit's digit. If the digits were reversed in order, the new number is 198 more than the original. What is the original number?

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1. original number:

let the unit digit be x
then the tens digit is x+1

since the sum of all 3 digits is 14
the hundreds digit must be 14 - x - (x+1)
= 13 - 2x

now the actual number, using place holder value, is
100(13-2x) + 10(x+1) + x
= 1300 - 200x + 10x + 10 + x
= -189x + 1310

the number reversed would be
100(x) + 10(x+1) + 13-2x
= 100x + 10x + 10 + 13 - 2x
= 108x + 23

now this number is supposed to be 198 more than the first number, that is

(108x + 23) - (-189x+1310) = 198
108x + 23 + 189x - 1310 = 198
297x = 1485
x = 5

so the unit digit is 5
the tens digit is x+1 = 6
the hundreds digit is 13-2x = 3
the original number was 365

check:
reversing it would be 563
is the difference equal to 198 ???

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2. yes, thank you.

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3. Amiin

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4. the sum of the digits of three digit number is 14 of hundreds and tens digits are reserved the resulting number is 90 more than the original number if the tens and units digit are resulting number is 27 more than the original number find the original number

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5. the sum of the digits of three digit number is 14 of hundreds and tens digits are reserved the r6esulting number is 90 more than the original number if the tens and units digit are resulting number is 27 more than the original number find the original number

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2. 👎
3. ℹ️
4. 🚩

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