maths

A number of two digit is such that four times the unit digit is five greater than trice the tense digit.when the digit are reserved,the number is increased by nine find the number.

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  1. If your question means:

    A two digits number is such that four times the unit digit is five times greater than the tens digit. When the digits are reversed, the number is increased by nine. Find the number?

    then

    a = the tens digit

    b = the unit digit

    Your number is:

    x = 10 a + b

    Four times the unit digit is five time greater than twice the tens digit means:

    4 b = 5 a

    When the digit are reserved new number is 10 b + a

    When the digit are reserved, the number is increased by nine means:

    10 b + a = x + 9

    Replace x with 10 a + b in this equation

    10 b + a = 10 a + b + 9

    Subtract b to both sides

    9 b + a = 10 a + 9

    Subtract a to both sides

    9 b = 9 a + 9

    Divide both sides by 9

    b = a + 1

    Now you must solve system:

    4 b = 5 a

    b = a + 1
    _______

    The solution is a = 4 , b = 5

    x = 10 a + b

    x = 10 ∙ 4 + 5

    x = 40 + 5

    x = 45

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