To solve for \( y \), the length of the rectangular room, we can start by letting \( y \) represent the length of the room. According to the problem, the width of the room is 5 feet less than the length, which can be expressed as \( y - 5 \).
The area of a rectangle can be calculated as the length multiplied by the width. Therefore, we can set up the equation for the area:
\[ y(y - 5) = 750 \]
This equation represents the area of the rectangle, where \( y \) is the length, and \( y - 5 \) is the width.
Now, let's analyze the options provided to identify which equations can be used to represent this situation:
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\( y(y + 5) = 750 \) - This is incorrect because it incorrectly uses \( y + 5 \) instead of \( y - 5 \) for the width.
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\( y^2 - 5y = 750 \) - This is a rearranged version of the correct equation \( y(y - 5) = 750 \). This can work to solve for \( y \).
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\( 750 - y(y - 5) = 0 \) - This is another rearrangement of the correct equation, moving \( y(y - 5) \) to one side. This can also work to solve for \( y \).
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\( y(y - 5) + 750 = 0 \) - This is incorrect, as it doesn't accurately represent the area equation.
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\( (y + 25)(y - 30) = 0 \) - This does not directly correspond to the problem as it's an unrelated factorization.
From the above analysis, the three equations that can be used to solve for \( y \) are:
- \( y^2 - 5y = 750 \)
- \( 750 - y(y - 5) = 0 \)
- The original equation \( y(y - 5) = 750 \), though not listed as an option.
So, from the choices that you provided, the ones that can be used to solve for \( y \) are:
- \( y^2 - 5y = 750 \)
- \( 750 - y(y - 5) = 0 \)
The first equation you provided does not apply, so you can only select these two. The options suggest using three, but without including the original area equation, you only find these two are valid from what's provided.
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