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, an essay worth 8 points each. how many essays questions are on the test? explain or show your work

The number of essay questions on the test were 9

Step-by-step explanation:

Given as :

Total number of questions in a test = 26

Total points for the 26 questions = 123

The point for each multiple choice questions = 3

The point for each essay questions = 8

Let The number of multiple choice questions = m

Let The number of essay questions = e

Now, According to question

Total number of questions in a test = number of multiple choice questions +  number of essay questions

Or, m + e = 26         .....A

Again

Total points for the 26 questions =  point for each multiple choice questions  ×  number of multiple choice questions + point for each essay questions × number of essay questions

i.e 3 × m + 8 × e = 123

Or, 3 m + 8 e = 123          .......B

Solving the equation we get

8 × ( m + e ) - (3 m + 8 e) = 8 × 26 - 123

Or, 8 m + 8 e - 3 m - 8 e = 208 - 123

Or,(8 m -  3m) + (8 e - 8 e) = 85

Or, 5 m + 0 = 85

∴  m =

i.e m = 17

So,The number of multiple choice questions = m = 17

Put the value of m into eq A

∵ m + e = 26

Or, e = 26 - 17

i.e e = 9

So, The number of essay questions = e = 9

Hence, The number of essay questions on the test were 9 . Answer