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.

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.

the correct answer is 828.07

69

step-by-step explanation: