twice the larger of 2 consecutive integers equal 15 less than 3 times the smaller

Question

twice the larger of 2 consecutive integers equal 15 less than 3 times the smaller

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    0
    2021-11-25T21:56:34+00:00

    Let’s take the first number as ‘x’ ( This would be the smaller number )

    Let’s take the second number as ‘x+1’ ( This would be the larger number )

    I have taken x and x+1 because both these numbers are consecutive.

    Twice the larger number :-

    … 2 ( x + 1 )

    … 2x + 2

    15 less than thrice the smaller number :-

    … 3x – 15

    The question states that these both values are equal. Hence,

    … 2x + 2 = 3x – 15

    … 2 + 15 = 3x – 2x

    … 17 = x

    The value of ‘x’ is 17

    ( The smaller number is 17 )

    Larger number :-

    … x + 1

    … 17 + 1

    … 18

    Hence, the numbers are 17 and 18.

    Hope my answer helps!!

    0
    2021-11-25T21:56:50+00:00

    Answer:

    the two integers are 17 and 18

    Step-by-step explanation:

    Let x represent the smaller integer. Then x+1 is the larger. The problem statement tells us

    … 2 × larger = -15 + 3 × smaller

    … 2(x+1) = -15 + 3x . . . substitute variable expressions for ‘larger’ and ‘smaller’

    … 2x +2 = 3x -15 . . . . . eliminate parentheses

    … 17 = x . . . . . . . . . . . . .add 15-2x

    The smaller integer is 17, so the larger is 18.

    _____

    Check

    2×18 = 36 = 3×17 -15 = 51-15

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