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Video: Stating the System of Inequalities That Describes a Given Situation

Bethani Gasparine

A shepherd wants to build a rectangular sheep barn. The length of the barn must be more than 88 m and its perimeter must be less than 253 m. Derive the system of inequalities that describes the situation, denoting the length of the barn by x and its width by y.

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Video Transcript

A shepherd wants to build a rectangular sheep barn. The length of the barn must be more than eighty-eight meters and its perimeter must be less than two hundred and fifty-three meters. Derive the system of inequalities that describe the situation, denoting the length of the barn by π‘₯ and the width by 𝑦.

It says the length of the barn must be more than eighty-eight meters. And the length is represented by π‘₯, so π‘₯ must be greater than eighty-eight. And the next thing it talks about is the perimeter, where we would add up all of the sides. There would be two π‘₯s and two 𝑦s, which we could rewrite using a GCF, a greatest common factor, of two. And it says, the perimeter must be less than two hundred and fifty-three. Therefore, two times π‘₯ plus 𝑦, the perimeter, is less than two hundred and fifty-three.