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Thread: 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.
    $\displaystyle p=1\text{ft.}^2\text{ of paint}$
    $\displaystyle w=1\text{ft.}^2\text{ of wallpaper}$

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

    And: $\displaystyle p+w=300$

    So: $\displaystyle w=300-p$

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

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

    Multiply: $\displaystyle 1.4p+180-0.6p\leq324$

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

    Subtract: $\displaystyle 0.8p+180\leq324$

    Subtract 180 from both sides: $\displaystyle 0.8p\leq144$

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