PLEASE HELP !!!!!!!!!! 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. 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. PLEASE HELP !!!!!!!!!! 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. 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.
The Correct Answer and Explanation is:
Given:
Alexia spends 3 minutes per math problem → Let xx be the number of math problems.
She spends 4 minutes per science problem → Let yy be the number of science problems.
Her total time is more than 60 minutes → This gives us the inequality: 3x+4y>603x + 4y > 60
We are given 4 options to test:
8 math, 9 science → 3(8)+4(9)=24+36=603(8) + 4(9) = 24 + 36 = 60 → Not greater than 60 ❌ Doesn’t satisfy the inequality.
4 math, 6 science → 3(4)+4(6)=12+24=363(4) + 4(6) = 12 + 24 = 36 ❌ Less than 60. Doesn’t satisfy the inequality.
0 math, 15 science → 3(0)+4(15)=0+60=603(0) + 4(15) = 0 + 60 = 60 ❌ Exactly 60. Not more than 60.
✅ Correct Answer:
Alexia completed 20 math problems and 10 science problems.
Explanation
This problem involves an inequality that represents the total time Alexia spent on her homework. Since she spends 3 minutes per math problem and 4 minutes per science problem, the time spent can be expressed as 3x+4y3x + 4y, where xx is the number of math problems and yy is the number of science problems.
The condition “Her homework took her more than 60 minutes” translates to the inequality: 3x+4y>603x + 4y > 60
This means the total minutes she spent must be greater than 60 — not equal to or less than.
To find which scenario could be true, we plug in the values from each of the four answer choices into the inequality.
In the first option, 8 math and 9 science give exactly 60 minutes. Since the inequality demands more than 60, this option is not valid.
The second option, with 4 math and 6 science, results in just 36 minutes — well below the minimum requirement.
The third option has Alexia completing 20 math and 10 science problems. This totals 100 minutes, which is well above 60, making this the only choice that satisfies the condition.
The fourth option again totals exactly 60 minutes, which is not greater than 60.
Therefore, the only possible and valid scenario is:
Alexia completed 20 math problems and 10 science problems.
