In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, David has scored 81, 92, and 74 on the first three. What range of scores on the fourth test will give David a B for the semester (an average between 80 and 89, inclusive)?Assume that all test scores have a non-negative value.
Express your answer in interval notation.

The answer in interval notation is ( 73 ,  100 )

Step-by-step explanation:

If we call x and y the lower and upper values for David to get an average of 80 and 89 respectively, we can calculate these two values solving a pair of equations:

(81  +  92  + 74  +  x ) / 4  = 80     ⇒   (247  +  x  )/4 = 80

247  +  x  =  320    ⇒    x  =  320 - 247

x  =  73

And

(81  +  92  + 74  +  y ) / 4  = 89     ⇒   ( 247  +  y ) / 4  =  89

247   +  y  =   356

y  =  356  -  247

y  =  109

But tests are a 100-point test

Then the answer in interval notation is ( 73 ,  100 )

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3

ou would have 12 of each