Answer:
There are 9 essay questions.
Step-by-step explanation:
Let x represent the number of multiple-choice questions and y represent the number of essay questions.
Given that the total question count is 26, we can derive the equation,
Additionally, the multiple-choice and essay questions carry values of 3 points and 8 points, respectively.
The overall points available in the test equal 123.
Thus, we set up the following equations:
x+y=26...........................(1)
3x+8y=123............................(2)
If we multiply equation (1) by 3 and subtract equation (2), we obtain:
5y = 45, leading to y = 9
Consequently, from x+y=26, we find x = 26 - y, resulting in x = 17.
Hence, the counts of multiple-choice and essay questions are 17 and 9, respectively.