To receive a C grade, a student must average more than 77 but less than or equal to 85. If Noah received a C in the course and had five grades of 73, 85, 75, 69, and 82 before taking the final exam, what were the possible grades for his final if there were 100 points possible? (Assume all six grades are weighted equally and let x
represent the unknown score.)

9514 1404 393

  78 < x ≤ 100

Step-by-step explanation:

The course final grade will be the average of 6 scores. We want that average to be in the range 77 to 85.

  course average = (73 +85 +75 +69 +82 +x)/6 = (384 +x)/6 = 64 +x/6

The desired range is ...

  77 < 64 +x/6 ≤ 85

  13 < x/6 ≤ 21

  78 < x ≤ 126

The maximum final exam score is 100, so possible grades are ...

  78 < x ≤ 100

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1