Let x and y represent the tens digit and ones digit of a two digit number, respectively. The sum of the digirs of a two digit numbet is 9. I

Question

Let x and y represent the tens digit and ones digit of a two digit number, respectively. The sum of the digirs of a two digit numbet is 9. If the digits are reversed, the new number is 27 more than the original number. What is the original number? *Write a system of equations *solve the systems of equations

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Emery 2 weeks 2021-11-20T19:33:18+00:00 1 Answer 0

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    2021-11-20T19:35:17+00:00

    Answer:

    The Original Number is 36

    Step-by-step explanation:

    Given:

    y is the number in units place

    x is the number in tens place

    Original Number = 10x+y

    x+y=9 is equation 1

    Now after interchanging the digits

    New number = 10y+x

    New Number = 27 + Original Number

    Substituting Valus in above equation we get.

    10y+x=27+10x+y\\10y-y+x-10x=27\\9y-9x=27\\9(y-x)=27\\y-x=\frac{27}{9}\\

    y-x=3 let this be equation 2

    Adding equation 1 and 2 we get

    (x+y=9)+(y-x=3)\\2y=12\\y=\frac{12}{2}\\y= 6\\

    Substituting value of y in equation 1 we get

    x+y=9\\x+6=9\\x=9-6\\x=3

    x=3 and y=6

    Original Number = 10x+y=10\times3+6=30+6=36

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