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Math Help - maximum area

  1. #1
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    maximum area

    The crawleys hallway has 300ft² of wall space. They recived an estimate of $1.40/ft² to paint a wall and 60˘/ft² to wallpaper a wall. With $324 to spend, what is the maximum area they can have painted if the rest has to be papered.

    I would greatly appreciate any help.
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  2. #2
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    Quote Originally Posted by begold91 View Post
    The crawleys hallway has 300ft² of wall space. They recived an estimate of $1.40/ft² to paint a wall and 60˘/ft² to wallpaper a wall. With $324 to spend, what is the maximum area they can have painted if the rest has to be papered.

    I would greatly appreciate any help.
    p=1\text{ft.}^2\text{ of paint}
    w=1\text{ft.}^2\text{ of wallpaper}

    The price of the whole thing is: 1.4p+0.6w\leq324

    And: p+w=300

    So: w=300-p

    Go back to the price equation: 1.4p+0.6w\leq324

    Substitute: 1.4p+0.6(300-p)\leq324

    Multiply: 1.4p+180-0.6p\leq324

    Group like terms: 1.4p-0.6p+180\leq324

    Subtract: 0.8p+180\leq324

    Subtract 180 from both sides: 0.8p\leq144

    Divide both sides by 0.8: \boxed{p\leq180}
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