Question

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.

Answer 1

Answer:

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:

$x+y=26...(1)$

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:

$3x+8y=123...(2)$

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

From equation (1) we will get,

$x=26-y$

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

$3*(26-y)+8y=123$

$78-3y+8y=123$

$78+5y=123$

Let us subtract 78 from both sides of our equation.

$78-78+5y=123-78$

$5y=45$

Let us divide both sides of our equation by 5.

$\frac{5y}{5}=\frac{45}{5}$

$y=9$

Therefore, there were 9 essay questions in the test.