Select the correct answer.
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 area of the original field is 300 square meters. Since the new addition is rectangular, its area can be represented as length times width. Let y represent the length of the new addition.
According to the problem, the length of the new addition is at least 10 meters more than twice the width. This can be written as:
y ≥ 2x + 10
The area of the entire practice field, including the new addition, must be no more than 1,200 square meters. This can be written as:
A = xy ≤ 1,200
Therefore, the system of inequalities that can be used to represent this situation is:
y ≥ 2x + 10
xy ≤ 1,200