sat-dog

Choice C is correct. Let a equal the number of 120-pound packages, and let b equal the number of 100-pound packages. It’s given that the total weight of the packages can be at most 1,100 pounds: the inequality represents this situation. It’s also given that the helicopter must carry at least 10 packages: the inequality represents this situation. Values of a and b that satisfy these two inequalities represent the allowable numbers of 120-pound packages and 100-pound packages the helicopter can transport. To maximize the number of 120-pound packages, a, in the helicopter, the number of 100-pound packages, b, in the helicopter needs to be minimized. Expressing b in terms of a in the second inequality yields , so the minimum value of b is equal to . Substituting for b in the first inequality results in . Using the distributive property to rewrite this inequality yields , or . Subtracting 1,000 from both sides of this inequality yields . Dividing both sides of this inequality by 20 results in . This means that the maximum number of 120-pound packages that the helicopter can carry per trip is 5.

Choices A, B, and D are incorrect and may result from incorrectly creating or solving the system of inequalities.