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 the solution.
The problem asks to identify a situation that could be true based on the given information. The information states that Alexia spent 3 minutes on each math problem and 4 minutes on each science problem, and her total homework time was “more than 60 minutes.”
First, let’s represent this 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 on math is 3x minutes, and the total time spent on science is 4y minutes. The total time for all homework is the sum of these two, 3x + 4y. Since the problem states this total time was “more than 60 minutes,” the correct inequality is 3x + 4y > 60.
The graph provided shows a dashed boundary line for the equation 3x + 4y = 60. A dashed line signifies a strict inequality (> or <), meaning that any combination of problems that falls directly on the line is not a valid solution. A valid solution must be a point in the region above this line.
Now, we can test each of the given options by plugging the values of x (math problems) and y (science problems) into our inequality 3x + 4y > 60.
- Option 1: 8 math problems and 9 science problems.
- x = 8, y = 9
- 3(8) + 4(9) = 24 + 36 = 60.
- This results in 60 > 60, which is false. This point lies on the boundary line, so it is not a solution.
- Option 2: 4 math problems and 6 science problems.
- x = 4, y = 6
- 3(4) + 4(6) = 12 + 24 = 36.
- This results in 36 > 60, which is false. This amount of work took less than 60 minutes.
- Option 3: 20 math problems and 10 science problems.
- x = 20, y = 10
- 3(20) + 4(10) = 60 + 40 = 100.
- This results in 100 > 60, which is true. This combination of problems takes more than 60 minutes and is a valid solution.
- Option 4: no math problems and 15 science problems.
- x = 0, y = 15
- 3(0) + 4(15) = 0 + 60 = 60.
- This results in 60 > 60, which is false. This point is the y-intercept of the boundary line and is not a solution.
Therefore, the only statement that could be true is the one where Alexia completed 20 math problems and 10 science problems, as it is the only option that results in a total time greater than 60 minutes.
