Joe wants to fence a rectangular pen for his goats. The length of the pen should be at least 60 ft, and the distance around should be no more than 260 ft. Which system of inequalities and graph represent the possible dimensions of the pen?
Let's assume the length of the pen is L and the width of the pen is W.
According to the problem, "the length of the pen should be at least 60 ft," so we can represent this as:
L ≥ 60
Also, "the distance around should be no more than 260 ft," so we can represent this as:
2L + 2W ≤ 260
Simplifying the second inequality, we have:
L + W ≤ 130
Therefore, the system of inequalities that represent the possible dimensions of the pen is:
L ≥ 60
L + W ≤ 130
To graph this system of inequalities, we represent each inequality on a coordinate plane. We will graph the first inequality as a horizontal line with a y-intercept of 60. Then we will graph the second inequality as a vertical line with an x-intercept of 130. The area where the graphs overlap will represent the possible dimensions of the pen.