Hi, there--

Problem:
A history exam included multiple choice questions that were worth 4 points each and 
true/false questions that were worth 2 points each. The highest score earned by a person in 
your class was 92.

a) Write an inequality that represents the number of multiple choice questions and true/false 
questions that could have been answered correctly by any member of your class.

b) Is it possible that some answered 20 multiple choice questions and 7 true/false questions 
correctly?

A Solution:

a) a) Write an inequality that represents the number of multiple choice questions and 
true/false questions that could have been answered correctly by any member of your class.

Let x be the number of correctly answered multiple-choice questions
Let y be the number of correctly answered true/false questions

The points earned by correctly answered multiple-choice questions is 4x.
The points earned by correctly answered true/false questions is 2y.

The inequality that represents the number of questions of each type that could have been 
answered is [multiple choice points earned] + [true/false points earned] is less than 92.



b) Is it possible that some answered 20 multiple choice questions and 7 true/false questions correctly?

20 multiple choice questions correctly answered corresponds to x = 20
7 true/false questions correctly answered corresponds to y = 7

We substitute this values into our inequality to see if the make the statement true.






This statement is false, so the scenario in problem b is not possible. 

We can check our work by referring to the original words of the problem. If a student got 20 
multiple choice questions and 7 true/false questions right, the score would be 80+14=94. 
The problem states that the highest score is 92, so a score of 94 is not possible.

Hope that helps!
Mrs. Figgy