<PRE><B>Question 251983</B>
First method

Let the total number of tests taken by Beth be x.
If Beth gets a 97 on her next math test, her average will be 90
If she gets 73, her average will be 87.
As of now,       90x - 97 = 87x-73
                 90x-87x  = 97-73
                       3x = 24
                        x = 8
So, the number of tests already undertaken = 8-1 = 7

Second Method
Let the number of tests already undertaken be x and 
    the total marks secured be n.
If Beth gets a 97 on her next math test, her average will be 90
      (n+97)/(x+1) = 90
              n+97 = 90(x+1)
              n+97 = 90x+90
              n+7  = 90x         ......(1)
Next,
     If she gets 73 in the next test, her average will be 87 
      (n+73)/(x+1) = 87
              n+73 = 87(x+1)
              n+73 = 87x+87
              n    = 87x + 14     ......(2)
  (1)-(2):
                 7 = 3x-14
                21 = 3x
                 7 = x 
So, the number of tests already undertaken = 7



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