Ask questions and get helpful answers.

A two digit number is seven times the sum of it's digits. The number formed by reversing the digits is 6 more than half of the original number. Find the difference of the digits of the given number .

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩

2 answers

  1. a = first number

    b = second number

    Your number = 10 a + b

    A two digit number is seven times the sum of it's digits meaans:

    10 a + b = 7 ( a + b )

    The number formed by reversing the digits is 10 b + a

    The number formed by reversing the digits is 6 more than half of the original number means:

    10 b + a = ( 10 a + b ) / 2 + 6

    Now you must solve system of two equations:

    10 a + b = 7 ( a + b )

    10 b + a = ( 10 a + b ) / 2 + 6
    ____________________________

    First equation:

    10 a + b = 7 a + 7 b

    Subtract 7 a to both sides

    3 a + b = 7 b

    Subtract b to both sides

    3 a = 6 b

    Divide both sides by 3

    a = 2 b

    Replace a with 2 b in equation:

    10 b + a = ( 10 a + b ) / 2 + 6

    10 b + 2 b = ( 10 • 2 b + b ) / 2 + 6

    12 b = ( 20 b + b ) / 2 + 6

    12 b = 21 b / 2 + 6

    Multiply both sides by 2

    24 b = 21 b + 12

    Subtract 21 b to both sides

    3 b = 12

    Divide both sides by 3

    b = 4

    a = 2 b

    a = 2 • 4

    a = 8

    a - b = 8 - 4 = 4

    Check result:

    A two digit number is seven times the sum of it's digits.

    Your number = 10 a + b = 10 • 8 + 4 = 84

    Sum of digits = 8 + 4 = 12

    84 = 7 •12

    The number formed by reversing the digits is 6 more than half of the original number.

    The number formed by reversing the digits is 10 b + a = 10 • 4 + 8 = 48

    Half of the original number =

    84 / 2 = 42

    48 = 42 + 6

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. a = first digit

    b = second digit

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Answer this Question

Related Questions

Still need help?

You can ask a new question or browse existing questions.