The Correct Answer and Explanation is:
The correct answer is Alexia completed 20 math problems and 10 science problems.
Here is a detailed explanation of how to arrive at the correct answer.
The problem states that Alexia spends 3 minutes on each math problem and 4 minutes on each science problem. Her total homework time was “more than 60 minutes.” We need to find which of the given scenarios is possible.
First, let’s represent the situation with a mathematical inequality. Let ‘x’ be the number of math problems and ‘y’ be the number of science problems. The total time spent can be calculated as:
(3 minutes/math problem) * (x math problems) + (4 minutes/science problem) * (y science problems)
Since the total time is “more than 60 minutes,” we can write the inequality:
3x + 4y > 60
The graph provided shows the boundary line for this inequality, which is the equation 3x + 4y = 60. Because the inequality is strictly “greater than” (>), the line is dashed, meaning any point on the line itself is not a solution. A valid solution must be a point (x, y) that lies in the shaded region above the line.
Now, we can test each of the multiple-choice options by substituting the values of x (math problems) and y (science problems) into our inequality.
- Alexia completed 8 math problems and 9 science problems:
Here, x = 8 and y = 9.
3(8) + 4(9) = 24 + 36 = 60.
The result is 60, which is not greater than 60. This point lies on the boundary line and is not a valid solution. - Alexia completed 4 math problems and 6 science problems:
Here, x = 4 and y = 6.
3(4) + 4(6) = 12 + 24 = 36.
The result is 36, which is not greater than 60. This is not a valid solution. - Alexia completed 20 math problems and 10 science problems:
Here, x = 20 and y = 10.
3(20) + 4(10) = 60 + 40 = 100.
The result is 100, which is greater than 60. This is a valid solution. - Alexia completed no math problems and 15 science problems:
Here, x = 0 and y = 15.
3(0) + 4(15) = 0 + 60 = 60.
The result is 60, which is not greater than 60. This point is the y-intercept of the boundary line and is not a valid solution.
Therefore, the only statement that could be true is that Alexia completed 20 math problems and 10 science problems, as this is the only option that results in a total time of more than 60 minutes.
