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Title:
Grants Fun Office - College Algebra
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Description:
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Athena started interning at an architecture firm, to learn the basics of
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designing and planning for the construction of new buildings. This isn't just
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any architecture firm, though. It just so happens to be the firm that designed
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the new office for Grant's gleaming glasses company. So we're going to go back
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in time to follow Athena through the work that went into creating Grant's
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awesome new space. Since Athena is just getting used to being a part of the
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world of architecture at all, the firm gave her a pretty simple project to work
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on first. Since Grant's such a fun guy, he wanted his office to have a separate
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space, just for having fun. Thus, the fun room, which Athena get's to plan.
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Grant has picked out a very special wallpaper that he wants used in this room.
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And has a pattern that he wants to make sure is fully expressed on every wall,
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but he also wants there to be natural light in the room. So he wants windows
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along two of the walls. However, since he's not willing to sacrifice any of that
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wallpaper pattern, the two walls with the windows on them are going to have to
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be longer than the other two walls. Let's call the distance from one wall to the
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edge of a window x. And assume that each of these windows are placed in the
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center of either wall. So that there's a distance of x on either side. Now,
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since Grant loves natural light so much, he wants these windows to be really
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big. In fact, he's already picked out, surprise, surprise, the exact windows
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that he wants. And they are each 3 meters across. Now, since we're calling each
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of these lengths of wall x, we know that this length of wall is going to be
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equal to the sum of those two. So this is just 2x. Now, the thing that Athena
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needs to figure out is how much carpet is going to need to be laid down in the
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fun room. So considering these side links and your understanding of, area of
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rectangles, please come up with an expression for the number of square meters of
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carpet Athena's going to need for this room. You could either multiply or not
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multiply out your answer.