The high school athletics department is installing a new rectangular addition to their current practice field. The length of the new addition will be at least 10 meters more than twice the width of the new addition. The original field has an area of 300 square meters. The area of the entire practice field, with the addition, must be no more than 1,200 square meters.
If A represents the area of the entire practice field, including the new addition, and x represents the width of the new addition, in meters, which system of inequalities can be used to represent this situation?

The system of inequalities that best represents this situation provided A denotes the area of the entire field is: [tex]\mathbf{\left \{ {{A\geq 2x^2+10x+300 } \atop {A \leq 1200}} \right. }[/tex]

What are word problems?

Word problems in mathematics are ways we can use variables, algebra notations, and arithmetic operations to solve real-life cases.

From the given information;

We have a new addition to the current rectangular field,

Let that new addition to the current rectangular field be x

The length of the new addition = 10x
Twice the width of the new addition = 2x²
The original area of the field = 300

From the above information, we can derive a quadratic equation:

2x² + 10x + 300

Also, we are given a constraint that the entire area of the practice field should be no more than 1200. i.e. It can be less than 1200 or equal to 1200.

Thus, the system of inequalities that best represents this situation provided A denotes the area of the entire field is:

[tex]\mathbf{\left \{ {{A\geq 2x^2+10x+300 } \atop {A \leq 1200}} \right. }[/tex]

Learn more about word problems in mathematics here:

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