Your teacher is giving you a test worth 100 points containing 40 questions. There are two-point and four-point questions on the test. How many of each ? Are on?

Question

Algebratic equation x=¿ &'d y=¿

Answer 1

Let:

   x = number of two-point questions

   y = number of four-point questions

 

Now, realize, the number of points obtained from the two-point questions is:

      (2 points/question)*(number of questions)      [questions cancel out, leaving points]

 

Translate:

  " test worth 100 points"   means:

     points from two-point questions  +  points from four-point questions = 100

                   2x                               +                 4y                            = 100      [eq1]

  "containing 40 questions"    means    x+y=40       [eq2]

 

Now, the easy math:

  Let's use the elimination method:

      2x    +    4y    =  100        [eq1]

      2x    +    2y    =   80         [eq2*2]

   ----------------------------   [elimination; subtract equations]

                    2y    =   20

                      y    =   10     [divide both sides by 2;  eq3]

 

      x     +     y      =    40     [eq2]

                    y      =    10     [eq3]

  ----------------------------    [elimination; subtract equations]

      x                    =     30

 

There are 30 two-point questions and 10 four-point questions.

 

Checking (very important):

   [eq1]  Is  2(30) + 4(10) = 100   ?

                   60  +  40  = 100   ?

                       100 = 100   ?yes

   [eq2]  Is  30 + 10 = 40   ?

                       40 = 40   ?yes