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? Explain your reasoning.

Answer 1

So if there are 26 questions on the test and each test is worth 123 points and only two types of questions on the test multiple choice worth three points and essays worth eight points so if you wanna do it the easy way just get the essay points 8 and divid it by the amount of points on the test which is 123 And you want to divide that and you will have your answer if you do the math correctly you will have 15 remainder three so there will be only 15 essay questions and one multiple-choice so yeah that is my answer well we can agree and disagree depends on you

Answer 2

Answer: 9 essay questions

Step-by-step explanation:

The test has 26 questions

The test is worth 123 points

The test has two types of questions:

Multiple choice worth 3 points each

Essays worth 8 points each

Let the number of multiple choice questions be, m, and the number of essay questions be , e.

This forms a simultaneous equation below:

m + e = 26 ... (i)

3m + 8e = 123 ... (ii)

Multiplying (i) by 3 and (ii) by 1 we get:

3m + 3e = 78 ... (i)

3m + 8e = 123 ... (ii)

Subtracting (ii) - (i) we get;

0m + 5e = 45

5e = 45

e = 45 ÷ 5 = 9

So there are 9 essay questions.

and;

m + 9 = 26

m = 26 - 9 = 17

There are also 17 multiple choice questions.