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: multiple choice worth 3 points each, and essays worth 8 points each. How many essay questions are on the test?

Answer 1

Number of essay questions are 9.

Explanation:

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

As, the total number of question are 26. We get,
`x+y=26`

Also, the multiple choice and the essay questions worth 3 and 8 points each.

Since, the total number of points of the test are 123.

So, we have,
`3x+8y=123`

So, the system of equations is,

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

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

Multiply (1) by 3 and subtracting by (2), we get,

5y = 45 i.e. y = 9

So, x+y=26 implies x = 26 - y i.e. x = 26 - 9 i.e x = 17

Thus, the number of multiple choice questions and essay questions are 17 and 9 respectively.