Diego’s history teacher writes a test for the class with 26 questions. the test is worth 123 points and has two types of questions: muiltiple choice worth 3 points each, and essays worth 8 points each. how many essay questions are in the test? explain or show you reasoning.

9 essay questions.

Step-by-step explanation:

Let x be the number of multiple choice questions and y be the number of essay questions.

We have been given that Diego’s history teacher writes a test for the class with 26 questions. We can represent this information in an equation as:

We are also told that multiple choice worth 3 points each, so total number of points for x questions will be 3x.

As essays worth 8 points each, so total number of points for y questions will be 8y.

Since the test is worth 123 points, so we can represent this information in an equation as:

Now we will use substitution method to solve system of linear equations.

From equation (1) we will get,

Substituting this value in equation (2) we will get,

Let us subtract 78 from both sides of our equation.

Let us divide both sides of our equation by 5.

Therefore, there were 9 essay questions in the test.

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