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n200080
21 day ago
12

Diego’s history teacher writes a test for the class with 26 questions. The test is worth 123 points and has two types of questio

ns: multiple choice worth 3 points each, and essays worth 8 points each. How many essay questions are on the test?
Mathematics
1 answer:
AnnZ [9K]21 day ago
5 0

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, x+y=26

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.

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