Step-by-step explanation:

Let's assume Esmeralda answers x number of 7-point questions and y number of 2-point questions.

Then, the total score she would get is:

7x (for each 7-point question) + 2y (for each 2-point question)

According to the problem, she needs to get at least 245 points. So, we can write an inequality:

7x + 2y >= 245

We also know that the total number of questions she can answer is at most 45:

x + y <= 45

Now, we need to find a solution that satisfies both the inequality and the equation above.

One possible way to approach this is to use trial and error. We can start by trying different values of x and y that satisfy the second inequality (x + y <= 45) and see if they also satisfy the first inequality (7x + 2y >= 245).

For example, if Esmeralda answers 30 7-point questions (x=30), she can answer at most 15 2-point questions (y=15) to satisfy the second inequality. Then, the total score she would get is:

730 + 215 = 255

This solution satisfies both inequalities, so Esmeralda would pass the examination if she answers 30 7-point questions and 15 2-point questions.

Another possible solution is to answer 35 7-point questions (x=35) and 10 2-point questions (y=10), which gives a total score of:

735 + 210 = 245

This solution also satisfies both inequalities, so Esmeralda would pass the examination if she answers 35 7-point questions and 10 2-point questions.

There may be other solutions as well, but these are two possible ones :))