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

9 essay questions.

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.

`(5y)/(5)=(45)/(5)`

`y=9`

Therefore, there were 9 essay questions in the test.