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A baker uses square prisms for her cake boxes. The height of each box is 5.5 inches, and the volume of each box must be 352 cubic inches. The equation below can be used to find the side length, [tex][tex]$x$[/tex][/tex], of the box:
[tex]$
5.5 x^2=352
$[/tex]

Which statement best describes the solutions to this equation?

A. The solutions are -16 and 16, which are both reasonable side lengths.
B. The solutions are -16 and 16, but only 16 is a reasonable side length.
C. The solutions are -8 and 8, which are both reasonable side lengths.
D. The solutions are -8 and 8, but only 8 is a reasonable side length.

Sagot :

GinnyAnswer
To determine the correct answer, let’s solve the equation step by step:

The given equation is:

[tex]\[ 5.5x^2 = 352 \][/tex]

1. Isolate [tex]\( x^2 \)[/tex]:

To isolate [tex]\( x^2 \)[/tex], we need to divide both sides of the equation by 5.5:
[tex]\[ x^2 = \frac{352}{5.5} \][/tex]

2. Simplify the fraction:

Divide 352 by 5.5:
[tex]\[ x^2 = 64 \][/tex]

3. Solve for [tex]\( x \)[/tex]:

To solve for [tex]\( x \)[/tex], take the square root of both sides of the equation:
[tex]\[ x = \sqrt{64} \quad \text{or} \quad x = -\sqrt{64} \][/tex]
[tex]\[ x = 8 \quad \text{or} \quad x = -8 \][/tex]

4. Interpret the solutions:

We have two solutions: [tex]\( x = 8 \)[/tex] and [tex]\( x = -8 \)[/tex].

Since side lengths cannot be negative in a real-world context such as this one, [tex]\( x = -8 \)[/tex] is not a reasonable solution. Therefore, the only reasonable side length is [tex]\( x = 8 \)[/tex].

Thus, the statement that best describes the solutions to this equation is:

The solutions are -8 and 8, but only 8 is a reasonable side length.
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