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6 December, 20:41

The units pf the digits of a two digits numeral is 8 if the digits are reversed the new number is 18 greater than the oringal number fund the oringal numeral

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  1. 6 December, 21:03
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    complete question:

    The sum of the digits of a two-digit numeral is 8. If the digits are reversed, the new number is 18 greater than the original number. How do you find the original numeral?

    Answer:

    The original number is 10a + b = 10 * 3 + 5 = 35

    Step-by-step explanation:

    Let

    the number = ab

    a occupies the tens place while b occupies the unit place. Therefore,

    10a + b

    The sum of the digits of two-digits numeral

    a + b = 8 ... (i)

    If the digits are reversed. The reverse digit will be 10b + a. The new number is 18 greater than the original number.

    Therefore,

    10b + a = 18 + 10a + b

    10b - b + a - 10a = 18

    9b - 9a = 18

    divide both sides by 9

    b - a = 2 ... (ii)

    a + b = 8 ... (i)

    b - a = 2 ... (ii)

    b = 2 + a from equation (ii)

    Insert the value of b in equation (i)

    a + (2 + a) = 8

    2a + 2 = 8

    2a = 6

    a = 6/2

    a = 3

    Insert the value of a in equation (ii)

    b - 3 = 2

    b = 2 + 3

    b = 5

    The original number is 10a + b = 10 * 3 + 5 = 35
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