test has twenty questions 100 point consists of x true-false questions4 pointsand y multiple choice8 points eachHow many of each type of question are ontest

Question

I need I better understanding of how one would evaluate this problem 

Answer 1

Let x = number of TF questions (4 points each)

     y = number of MC questions (8 points each)

 

Here is some very important information:

   (points per question)*(number of questions) = points     [because questions cancel out]

 

"test has twenty questions"    means    x+y=20    [eq1]

 

"100 points"    means

   (number of points for TF questions) + (number of points for MC questions) = 100

                       4x                            +                    8y                               =100        [eq2]

 

Substitution Method:

   Solve for a variable usinf [eq1]:         x=20-y

   Substitute for x in [eq2]:

             4(20-y)   +   8y   =  100

             80 - 4y + 8y = 100

             80 + 4y = 100

                4y = 20

                 y = 5

There are 5 multiple-choice questions.

 

Use either [eq1] oe [eq2] to find the value of x:

      x + y = 20

      x + 5 = 20

        x = 15

There are 15 True-False questions.

 

Check:     Is 4(15)  +  8(5)  = 100   ?

                      60  +  40  =  100   ?

                         100 = 100   ?yes