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?

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  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 ???

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. yes, thank you.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. Amiin

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  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

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  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

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the

  2. math

    While adding ten two-digit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the

  3. math

    Neelesh is fond of playing number games. Once when his friends were present he challenged them. He said that he has thought of a five-digit number and anyone who guesses it correctly can use his cycle for a full day. ‘To help

  4. math

    Form the greatest possible 5-digit number using the clues.All five digits are different. None of the five digit are 1.The digit in the ten thousands place is greater than 7.The sum of all five digit is 18.The greatest digit is

  1. Math

    John chooses a 5-digit positive integer and deletes one of its digits to make a 4-digit number. The sum of this 4-digit number and the original 5-digit number is 52713. What is the sum of the digits of the original 5-digit number?

  2. Mathe

    The number has two digits. Both of the digits are even.the digit in the tens place is greater that the digit in the unit (or ones) place.the units (or ones digit) is not in the three times table. The tens digit is not double the

  3. mathematics

    I am a five digit number. Digit at ones place is same as digit at tens place and their sum is 2. Digit at ten thousands place is the largest one digit even number. Face value of the digit at hundreds place is 3. Difference of

  4. Algebra math.

    1) the sum of the digits of a two digit number is 9. The value of the number is 12 times the tens digit. Find the number. 2) the sum of the digits of a two digit number is 12. If 15 is added to the number the result is 6times the

  1. Math

    What is the three digit mystery number? Clues: It is less than 300, the tens digit is 4 more than the hundreds digit, the sum of the digits is 9, the hundreds digit is 2 less than the ones digit.

  2. math

    Find a six-digit even number containing no zeros and no repeating digits in which the first digit is four more than the second digit, the third digit is one less than the sixth digit, and the fourth and fifth digits when read as a

  3. math

    The number has 6 digits. The nuber is less than 300000. 10 is a factor of the number. The hundred thousands and ten thousands digit are the same and are odd. The tens digit is a cube number and is one more than the thousands

  4. math

    this code has five digit 1,2,3,4,5. the first digit plus the second digit is equal to the third digit the second digit twice times the first digit the second digit is half the fourth digit and the fifth digit is the sum of the

View more similar questions or ask a new question.