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Answer:
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
<u>Now, According to question</u>
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