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 or show your reasoning.

Number of essay questions = 9

Step-by-step explanation:

The test has 26 questions

The test is worth 123 points

The test has two types of questions:

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 17 multiple choice questions.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

26?

step-by-step explanation: