The sum of the digits of a three digit number is 20. The middle digit is equal to one fourth the sum of the other two. If the order of degree is reversed the number increases by 198. Find the original number

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. The maximum sum of two digits in the number (first and last) can be 18. Thus, the middle digit cannot be larger than 4 (since that would be larger than 1/4th the largest sum).

    Since reversing the number increases it, the third digit is larger than the first. The first digit is two less than the third digit, since that condition is necessary for their difference to end with an 8.

    The number is 749.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. algebra solution:
    let the unit digit be z
    let the tens digit be y
    let the hundred digit be x
    x+y+z = 20

    y = (1/4)(x+z)
    4y = x+z

    original number is 100x + 10y + z
    reversed number is 100z + 10y + x

    difference of those two is 198
    100x + 10y + z - 100z - 10y - x = 198
    99x - 99z = 198
    x - z = 2
    z = x-2 , so y = (x + x-2)/4

    in x+y+z = 20
    x + (2x-2)/4 + x-2 = 20
    8x + 2x-2 - 8 = 80
    10x = 90
    x = 9
    then z = 7
    and 4y = 16 ---> y = 4

    The numbers are 947 and 749 , as Arora also found.
    (I simply took the difference between the numbers to be 198, I should have reversed the order of subtraction)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  3. Very nice bc

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. maths

    a number consist of two digits of which tens digit exceeds the unis digit by 7 the number itself is equal to 10 times the sum of its digit find the number

  2. math

    When this 3 digit number is rounded to the nearest hundred, it rounds to 300. The digit in the ones place is 4. The sum of the digits in the 3 digit number is 11. What is the number?

  3. Maths

    In A Two Digit Number, The Sum Of The Digits Is 14. Twice The Tens Digit Exceeds The Units Digit By One.Find the Numbers.

  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. 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

  3. 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

  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

    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

  2. Math

    A number rounds off 4000 the digit in the hundred places is twice the digit in the tens place. The sum of the digit is 12 . the number uses only two different digits .find the number

  3. algebra

    the units digit of a 2-digit number exceeds twice the tens digit by 1. find the number if the sum of its digits is 10. Please help i am completley lost!!

  4. Algebra

    The sum of the digits of a three-digit number is 11. If the order of the digits is reversed, the number is decreased by 396. The tens digit is one half of the hundreds digit. Find the number.

View more similar questions or ask a new question.