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

Question Video: Stating the System of Inequalities That Describes a Given Situation Mathematics • First Year of Secondary School

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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 88 meters and its perimeter must be less than 253 meters. Derive the system of inequalities that describes the situation, denoting the length of the barn by 𝑥 and its width by 𝑦.

Let’s start by highlighting what we know. We can use 𝑥 to represent the length of the barn, which will be more than 88 meters, and the width of the rectangular barn will be represented by the variable 𝑦. However, we haven’t been told anything specifically about 𝑦, but we know that the perimeter will be less than 253 meters. Thinking a bit more about the perimeter of a rectangular sheep barn, if the length is 𝑥 and the width is 𝑦, we know that the perimeter of a rectangle is equal to two times the length plus the width.

The perimeter of the sheep barn must be less than 253 meters. We know that two times the length plus the width is equal to the perimeter. Therefore, we can say two times 𝑥 plus 𝑦 must be less than 253. Additionally, we know that the length 𝑥 must be greater than 88 meters, which means we can write an inequality 𝑥 is greater than 88. You might think we’re finished as we’ve described this system with two inequalities. However, we will also have to define our width with one more inequality. We want to make sure that if we were to solve this equation, we would only be dealing with positive values. And that means we have to define 𝑦 as greater than zero.

Therefore, the system of inequalities that describes this situation is 𝑥 greater than 88, 𝑦 greater than zero, and two times 𝑥 plus 𝑦 is less than 253.

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