Translate the following situation into an inequali

“Charlie would like to pack one less outfit than Jane for their trip. Loretta would like to bring five outfits less than twice what Jane packs. Due to space in the suitcase, they are limited to a total of 24 outfits. How many outfits can they each pack?”

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  1. first, we represent the unknowns using variables.
    let x = outfits that Jane packed
    let x-1 = outfits that Charlie packed
    let 2x-5 = outfits that Loretta packed
    since "limited to a total of 24 outfits", it means that the maximum number of outfits is 24:
    x + (x-1) + (2x-5) <= 24
    note: <= means less than or equal to
    solving,
    4x - 6 <= 24
    4x <= 30
    x <= 7.5
    but since outfits cannot be a decimal/fraction, we take
    x = 7 (the max number of outfit that Jane can pack)
    and thus,
    x-1 = 6 (max number of outfit that Charlie can pack)
    2x-5 = 9 (max number of outfit that Loretta can pack)

    hope this helps~ :)

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  2. If Jane packs x "outfits", the total number packed is
    x + (x-1) + (2x -5) =or< 25

    4x -6 =or< 25
    4x <or= 31, and x must be an integer

    x <or= 7 is Jane's number
    6 is Charlie's maximum
    9 is Loretta's maximum

    They will not use up the available space if they stick to the rules relative to each other. There is room for two more outfits, unless I made a mistake along the way. See what you get

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