A rancher wants to build a rectangular pen for her animals. She decides that the length, l, of one side of the pen should be at most 60 feet, the width, w, of one side of the pen should be at least 30 feet, and the perimeter of the pen should be at most 200 feet. Which of the following systems of inequalities best models the situation described? Choose 1 answer: (A) {[l+w = 30],[l = 200],[w = 60]:} c) {[l+w = 30],[l = 200],[w = 30],[l

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A rancher wants to build a rectangular pen for her animals. She decides that the length, l, of one side of the pen should be at most 60 feet, the width, w, of one side of the pen should be at least 30 feet, and the perimeter of the pen should be at most 200 feet. Which of the following systems of inequalities best models the situation described? Choose 1 answer: (A) {[l+w <= 200],[w >= 30],[l <= 60]:} (B) {[l+w >= 200],[w <= 30],[l >= 60]:} c) {[l+w <= 100],[w >= 30],[l <= 60]:} (D) {[2l+2w >= 200],[w >= 30],[l <= 60]:}

Bytelearn · Accepted Answer

Define Length Constraint: The rancher wants the length of one side of the pen to be at most 60 feet. This means the length, l, should be less than or equal to 60. So, we have the inequality l <= 60.Define Width Constraint: The width of one side of the pen should be at least 30 feet. This means the width, w, should be greater than or equal to 30. So, we have the inequality w >= 30.Define Perimeter Constraint: The perimeter of the pen should be at most 200 feet. The formula for the perimeter, P, of a rectangle is P = 2l + 2w. Since the perimeter should be at most 200 feet, we have the inequality 2l + 2w <= 200.Check Given Options: Now, we need to check which of the given options matches the inequalities we have derived. Option (A) says l + w <= 200, which is incorrect because the perimeter is 2l + 2w, not l + w. Option (B) has inequalities that are the opposite of what we need. Option (C) has the incorrect perimeter inequality, as it should be 2l + 2w <= 200, not l + w <= 100. Option (D) has the correct perimeter inequality 2l + 2w <= 200, the correct width inequality w >= 30, and the correct length inequality l <= 60.

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