To analyze the situation, we can set up the problem with variables to represent the number of multiple choice questions (let's say \(x\)) and the number of discussion questions (let's say \(y\)) that Alex can answer in the allotted 60 minutes.
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Multiple Choice Questions: It takes 2 minutes to answer each question.
- Therefore, if Alex answers \(x\) multiple choice questions, the time taken will be \(2x\) minutes.
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Discussion Questions: It takes 5 minutes to answer each question.
- Therefore, if Alex answers \(y\) discussion questions, the time taken will be \(5y\) minutes.
Given that the total time Alex can spend is 60 minutes, we can create the equation: \[ 2x + 5y \leq 60 \]
To visualize this, we can rearrange the equation to express \(y\) in terms of \(x\): \[ 5y \leq 60 - 2x \] \[ y \leq \frac{60 - 2x}{5} \] \[ y \leq 12 - \frac{2}{5}x \]
This equation represents a straight line where the y-intercept is 12 and the slope is -2/5. This means that as the number of multiple choice questions \(x\) increases, the maximum number of discussion questions \(y\) decreases.
Now, the graph that represents this relationship should start at the point (0, 12) on the y-axis (where Alex answers no multiple choice questions, but can answer up to 12 discussion questions) and should decrease towards the x-axis. The x-intercept (when \(y = 0\)) occurs when \(2x = 60\), or \(x = 30\) (where he answers no discussion questions).
Identifying the Correct Graph:
- The graph should show a downward sloping line starting from (0, 12) and crossing the x-axis at (30, 0).
- It should also clearly identify the feasible region that satisfies \(2x + 5y \leq 60\).
Without seeing the actual graphs J, K, L, or M, I can't specify which one is correct. But you would look for a graph that fits this description:
- It has a y-intercept of 12 and an x-intercept of 30, with a downward slope.
If you find that graph among J, K, L, or M, that will be the representation of the number of questions Alex can answer given his constraints.
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