The sum of two integers is 33. The larger is 6 more than twice the smaller. Find the two integers.

Question

The sum of two integers is 33. The larger is 6 more than twice the smaller. Find the two
integers.

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Verity 1 year 2021-08-31T22:17:00+00:00 2 Answers 8 views 0

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    0
    2021-08-31T22:18:26+00:00

    first we called x is the smaller number
    next we have larger number is 2x+6
    =>we have:2x+6+x=33
    <=>x=9
    so we have the larger number is 33-9=24

    0
    2021-08-31T22:18:55+00:00

    Answer:

    24 and 9

    Step-by-step explanation:

    Hi there!

    Let x be equal to the larger integer.

    Let y be equal to the smaller integer.

    1) Construct equations

    1. [tex]x+y=33[/tex] (The sum of two integers is 33)
    2. [tex]x=6+2y[/tex] (The larger is 6 more than twice the smaller)

    2) Solve for one of the integer

    Isolate x in the first equation

    [tex]x+y=33\\x=33-y[/tex]

    Plug the first equation into the second

    [tex]33-y=6+2y[/tex]

    Combine like terms

    [tex]33-6=2y+y\\27=3y\\9=y[/tex]

    Therefore, the smaller integer is 9.

    3) Solve for the other integer

    [tex]x+y=33[/tex]

    Plug in y (9)

    [tex]x+9=33\\x=33-9\\x=24[/tex]

    Therefore, the larger integer is 24.

    I hope this helps!

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