The inequality given is \(3x + 4y > 60\), where \(x\) is the number of math problems and \(y\) is the number of science problems. To determine which statement could be true, we need to check which combination of \(x\) and \(y\) satisfies the inequality.

1. For 8 math problems and 9 science problems:
   \[3( 8) + 4( 9) = 24 + 36 = 60\]
   Since \(60\) is not greater than \(60\), this combination does not satisfy the inequality.
2. For 4 math problems and 6 science problems:
   \[3( 4) + 4( 6) = 12 + 24 = 36\]
   Since \(36\) is not greater than \(60\), this combination does not satisfy the inequality.
3. For 20 math problems and 10 science problems:
   \[3( 20) + 4( 10) = 60 + 40 = 100\]
   Since \(100\) is greater than \(60\), this combination satisfies the inequality.
4. For no math problems and 15 science problems:
   \[3( 0) + 4( 15) = 0 + 60 = 60\]
   Since \(60\) is not greater than \(60\), this combination does not satisfy the inequality.

Supplemental Knowledge

Linear inequalities are expressions that show the relationship between two variables with an inequality sign. In this case, the inequality \(3x + 4y > 60\) represents the time Alexia spent on her homework, where \(x\) is the number of math problems and \(y\) is the number of science problems.
The boundary line for this inequality is given by \(3x + 4y = 60\). Points on this line represent combinations of math and science problems that take exactly 60 minutes to complete. Points above this line (where \(3x + 4y > 60\)) represent combinations that take more than 60 minutes.

Knowledge in Action

Imagine setting out on your study schedule, allotting each subject different amounts of time according to its difficulty or your interest. By setting time limits for each, you can ensure a balanced study session without overwork. This approach helps manage time efficiently while improving academic performance.
Spending additional time on topics where you struggle can help strengthen weaker areas without jeopardizing overall progress. This strategy allows students to gain improved results in areas they were previously struggling with without hindering overall development.

Understanding how to manage study time using linear inequalities can significantly enhance your academic performance. At UpStudy, we provide tools and resources that help you master these concepts effectively.
For detailed guidance on algebraic inequalities,explore UpStudy’s Algebra inequalities calculator today!