Question

Jim wants to fence a rectangular pen for his chickens. The length of the pen should be at 78 feet and the perimeter

should be no more than 412 feet. Which system of inequalities represent the possible dimensions of the pen? (1 point)
y ≥ 78
2x + 2y ≥ 412
y ≤ 78
2x + 2y ≤ 412
y ≤ 78
2x + 2y 2 412
y ≥ 78
2x + 2y ≤ 412

Answer 1

The system of inequalities representing the possible dimensions of the pen is y ≥ 78 and x ≤ 128.

Step-by-step explanation:

To represent the possible dimensions of the pen, we need to determine the range of values for the width of the pen. Let's assume the width of the pen is x. The length of the pen is given as 78 feet, so the length equation is:

Length = 78 feet

The perimeter equation is given as:

Perimeter = 2x + 2(78) ≤ 412

By simplifying the perimeter equation, we get:

2x + 156 ≤ 412

Subtracting 156 from both sides of the equation gives:

2x ≤ 412 - 156

2x ≤ 256

Finally, dividing both sides of the equation by 2 gives:

x ≤ 128

Therefore, the system of inequalities representing the possible dimensions of the pen is:

y ≥ 78

x ≤ 128