Question

A farmer wants to fence a rectangular habitat for goats. The length (y) of the habitat has to be at least 80 feet. The farmer currently has 310 feet of fencing available to use on the habitat. The system of inequalities below models this problem situation, where x represents the width of the habitat (in feet) and y represents the length of the habitat (in feet). y≥80 2x+2y≤310 Which of the following is a true statement? a. If the farmer makes a rectangular habitat with a length of 60 feet, the width needs to be 80 feet. b. The farmer can make a habitat that is 75 feet long and 60 feet wide. c. The farmer does not have enough fencing to enclose a rectangular habitat that is 80 feet long. d. The farmer can make a habitat that is 40 feet wide and 100 feet long.

Answer 1

d. The farmer can make a habitat that is 40 feet wide and 100 feet long.

Explanation:

The attached graph shows the inequalities and the various answer choices. The existence of the doubly-shaded area shows that answer choice C is false.

The appropriate choice is ...

d. The farmer can make a habitat that is 40 feet wide and 100 feet long.