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 :
To determine which statement could be true based on Alexia’s homework situation, we need to analyze the inequality given by the equation (3x + 4y > 60), where (x) represents the number of math problems and (y) represents the number of science problems. The coefficients (3 and 4) indicate the time spent on each problem: 3 minutes for math and 4 minutes for science.
First, we can rewrite the inequality:
[
3x + 4y > 60
]
This tells us that the total time spent on math and science problems must exceed 60 minutes.
Now, let’s analyze each of the provided statements:
- Alexia completed 8 math problems and 9 science problems.
- Calculation:
[
3(8) + 4(9) = 24 + 36 = 60
] - This does not satisfy (3x + 4y > 60).
- Alexia completed 4 math problems and 6 science problems.
- Calculation:
[
3(4) + 4(6) = 12 + 24 = 36
] - This also does not satisfy (3x + 4y > 60).
- Alexia completed 20 math problems and 10 science problems.
- Calculation:
[
3(20) + 4(10) = 60 + 40 = 100
] - This satisfies (3x + 4y > 60).
- Alexia completed no math problems and 15 science problems.
- Calculation:
[
3(0) + 4(15) = 0 + 60 = 60
] - This does not satisfy (3x + 4y > 60).
From the above analysis, the only statement that satisfies the inequality (3x + 4y > 60) is: Alexia completed 20 math problems and 10 science problems.
In conclusion, Alexia must complete a combination of math and science problems that exceeds 60 minutes of total work. The chosen statement accurately reflects a scenario where the time spent working on her homework meets the requirement, illustrating the relationship between the number of problems completed and the time taken for each type of problem. This reinforces the importance of understanding inequalities in practical situations like homework completion.