Please answer this question with an equation

Question

a math test has a total score of 96 points. there are 24 multiple choice questions and 3 short answer questions. Each short answer question is worth 5 more points than each multiple choice questio. How much is each multiple choice question worth?

(I typed the question wrong the first time oops)

Answer 1

Let y = points for each multiple choice question

      x = points for each short answer questions

 

Remember:  

   points for each group of question = (number of questions)*(points per question)

 

"a math test has a total score of 96 points"   means that

     points for multiple choice questions    +   points for short answer questions   =    96

                 24x                                      +        3y                                          =  96

 

"How much is each multiple choice question worth?"     means   solve for y

         3y = 96 - 24x

          y = 32 - 8x

 

[ note: we have assumed an equal number of points per each type of question]

Answer 2

To create the equation think of how tests are graded.

It's the number of questions times the value of each question that add up to the total test value.
Let x = the value of the multiple choice questions, and y = the value of the long form questions.

So to write your equation, we'd write:
24x + 3y = 96

Points of multiple choice + points to long form = total test points of 96.

 

Solving for y, we'd isolate y by moving the 24 to the other side thru subtraction:

3y = -24x+96

To express this as 1y, we'd divide by 3.

y = -8x + 32

Noting that both x and y must be >0. 

Answer 3

There is no way to answer the question with the information given, because we don't know if each multiple choice question is worth the same amount of points as each short answer question.

 

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However, IF WE ASSUME THAT ALL QUESTIONS ARE WORTH THE SAME NUMBER OF POINTS, then we can solve in the following way:

 

Let x = the total number of questions = 24 + 3 = 27

Let y = the total number of points = 96

 

Then the point value of each question is 96/27 = 3.56 (after rounding)

 

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However, if we assume that all multiple choice questions are worth the same number of points, and each short answer question is worth the same (but different from multiple choice) number of points, then we can solve in the following way:

 

Let x = the point value of one multiple choice question

Let y = the point value of one short answer question

 

Since there are 24 multiple choice questions and 3 short answer questions, we know the following:

 

24 * x + 3 * y = 96

 

Since the problem doesn't give us x nor y, you can plug in whatever value you like for x and solve for y.