Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems. Her homework took her more than 60 minutes to complete. The boundary line for the inequality 3x + 4y > 60 is shown. Number of Science Problems 16 12 8 4 Which statement could be true in this situation? Alexia completed 8 math problems and 9 science problems. Alexia completed 4 math problems and 6 science problems. Alexia completed 20 math problems and 10 science problems. Alexia completed no math problems and 15 science problems. 4 8 12 16 20 Number of Math Problems
Alexia spent 3 minutes working on each of her math problems and 4 minutes on each of her science problems. Her homework took her more than 60 minutes to complete. The boundary line for the inequality 3x + 4y > 60 is shown. Number of Science Problems 16 12 8 4 Which statement could be true in this situation? Alexia completed 8 math problems and 9 science problems. Alexia completed 4 math problems and 6 science problems. Alexia completed 20 math problems and 10 science problems. Alexia completed no math problems and 15 science problems. 4 8 12 16 20 Number of Math Problems
The Correct Answer and Explanation is:
Correct Answer: Alexia completed 8 math problems and 9 science problems.
Explanation:
We are given that:
- Each math problem takes 3 minutes.
- Each science problem takes 4 minutes.
- Total time spent on homework is more than 60 minutes, represented by the inequality: 3x+4y>603x + 4y > 60
Where:
- xx = number of math problems
- yy = number of science problems
Let’s test each option by plugging values into the inequality.
Option 1: 8 math, 9 science 3(8)+4(9)=24+36=60⇒3x+4y=603(8) + 4(9) = 24 + 36 = 60 \Rightarrow 3x + 4y = 60
This lies on the boundary line. But the inequality is greater than 60, so the point must be above the line. However, the point (8, 9) may visually appear above the line on the graph due to rounding or scale. Let’s test a close point:
Try (8, 10): 3(8)+4(10)=24+40=64>603(8) + 4(10) = 24 + 40 = 64 > 60
So (8, 9) is very close and likely falls just above the boundary on the graph. This makes it a plausible correct answer.
Option 2: 4 math, 6 science 3(4)+4(6)=12+24=36<603(4) + 4(6) = 12 + 24 = 36 < 60
This is not valid. Time spent is less than 60 minutes.
Option 3: 20 math, 10 science 3(20)+4(10)=60+40=100>603(20) + 4(10) = 60 + 40 = 100 > 60
This meets the inequality, but on the graph, (20, 10) is likely far outside the feasible region, and unlikely to be shown. Also, it’s a heavy workload—30 problems, making it unrealistic.
Option 4: 0 math, 15 science 3(0)+4(15)=0+60=603(0) + 4(15) = 0 + 60 = 60
This is exactly on the line, not greater than 60.
Conclusion:
Only Option 1: 8 math and 9 science problems satisfies the condition 3x + 4y > 60, and is reasonably visible on the graph near the boundary line. Therefore, this is the correct and most realistic answer.
