The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 equals 4 times the original n

Question

The sum of the digits of a 2-digit number is 7. If the digits are reversed, the new number increased by 3 equals
4 times the original number. Find the original number.​

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Ayla 2 weeks 2021-11-15T09:26:53+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-11-15T09:28:27+00:00

    Answer:

    Let the original number be

    yx

    ; i.e., 10y+x. We know x+y=7. The number obtained by reversing the digits in

    xy

    , i.e., 10x+y. The second condition gives 10x+y−2=2(10y+x). Thus we have two equations:

    x+y=7….(1)

    8x−19y=2….(2)

    Multiply the equation (1) by 19 and get

    19x+19y=133.

    Adding this to (2), we obtain 27x=135. This gives x=5. Hence y=7−x=7−5=2.

    The required number is 25.

    Step-by-step explanation:

    x+y = 7, or

    y = 7-x

    Let the number be 10x+y

    10y+x = 4(10x+y)-3, or

    10(7-x)+x = 4(10x+7-x) -3

    70 -10x+x = 40x+28–4x-3

    40x-4x+10x-x = 70–28+3

    45x = 45

    x=1 and y = 6.

    The numbers are 16 and 61. Answer

    0
    2021-11-15T09:28:52+00:00

    LET THE Tens DIGIT NUMBERS BE X

    AND ONES DIGIT NUMBER BE Y

    ATQ

    ORIGINAL NUMBER = 10X+Y

    x+y=71

    IF DIGITS ARE REVERSED THEN

    NUMBER FORMED

    10Y+X+3 = 4(10X+Y)

    10Y+X+3=40X+4Y

    6Y+3=39x2

    we have 2 equations solving these

    we get

    6y+3=39x

    6x+6y=42

    -45x=-45

    x=1

    putting in equation 1 weget

    y=6

    hence the original no is 10×1+6

    =16

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