Modded SAT Question Bank
by Abdullah Mallik dedicated to DPT SAT Batches and Someone Special | GitHub
We're excited to announce that we've launched a new and improved question bank with enhanced features and a more user-friendly interface.
To access the new question bank, please visit OnePrep.
We believe that this new platform will provide you with a better overall experience. Thank you for your continued support!
Test
Math
Domain
Algebra
Skill
Linear inequalities in one or two variables
Difficulty
Medium
ID: f224df07
Modded SAT Question Bank by Abdullah Mallik

A cargo helicopter delivers only 100-pound packages and 120-pound packages. For each delivery trip, the helicopter must carry at least 10 packages, and the total weight of the packages can be at most 1,100 pounds. What is the maximum number of 120-pound packages that the helicopter can carry per trip?

  1. 2

  2. 4

  3. 5

  4. 6

Toggle Answer

Tip: Press CTRL/Command to toggle answer
Correct Answer: C
Rationale

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 120 a, plus 100 b, is less than or equal to 1,100 represents this situation. It’s also given that the helicopter must carry at least 10 packages: the inequality a, plus b, is greater than or equal to 10 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 b is greater than or equal to, 10 minus a, so the minimum value of b is equal to 10 minus a. Substituting 10 minus a for b in the first inequality results in 120 a, plus 100, times, open parenthesis, 10 minus a, close parenthesis, is less than or equal to 1,100. Using the distributive property to rewrite this inequality yields 120 a, plus 1,000, minus 100 a, is less than or equal to 1,100, or 20 a, plus 1,000, is less than or equal to 1,100. Subtracting 1,000 from both sides of this inequality yields 20 a, is less than or equal to 100. Dividing both sides of this inequality by 20 results in a, is less than or equal to 5. 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.

Question Difficulty: Medium
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
1 / 27 Next