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:
The correct answer is: Alexia completed 8 math problems and 9 science problems.
Explanation
We are given the inequality: 3x+4y>603x + 4y > 60
where:
- xx = number of math problems (3 minutes each)
- yy = number of science problems (4 minutes each)
This inequality represents the condition that Alexia spent more than 60 minutes on homework. We are to test which option satisfies this condition.
Let’s plug each choice into the inequality:
Option A: 8 math, 9 science 3(8)+4(9)=24+36=60→ Not greater than 60, but equal3(8) + 4(9) = 24 + 36 = 60 \quad \text{→ Not greater than 60, but equal}
But the problem says “more than 60”, not just 60. So this seems false at first glance. However, note: this is the boundary line (3x + 4y = 60). Since the problem says the boundary is shown, and we are to identify a point above it (which satisfies 3x+4y>603x + 4y > 60), we need to test slightly beyond.
Let’s test Option A more carefully:
Try 8 math and 9 science again: 3(8)+4(9)=24+36=60⇒exactly on the boundary line3(8) + 4(9) = 24 + 36 = 60 \Rightarrow \text{exactly on the boundary line}
So this one is NOT valid because it’s not greater than 60, only equal.
Option B: 4 math, 6 science 3(4)+4(6)=12+24=36→ Too small3(4) + 4(6) = 12 + 24 = 36 \quad \text{→ Too small}
Reject
Option C: 20 math, 10 science 3(20)+4(10)=60+40=100→ Greater than 603(20) + 4(10) = 60 + 40 = 100 \quad \text{→ Greater than 60}
Valid. Keep for now
Option D: 0 math, 15 science 3(0)+4(15)=0+60=60→ Equal only, not > 603(0) + 4(15) = 0 + 60 = 60 \quad \text{→ Equal only, not > 60}
Reject
So now compare the valid ones:
Only Option C (20 math, 10 science) is fully correct and satisfies the inequality.
🟩 Final Correct Answer: Alexia completed 20 math problems and 10 science problems.
This is the only choice that results in more than 60 minutes of homework time.
