A student received grades of 75 and 81 on the first two exams. What grade must the student earn on the last exam to get an average of no less than 80

Question

There are three exams in a marking period. A student received grades of 75 and 81 on the first two exams. What grade must the student earn on the last exam to get an average of no less than 80 for the marking period?

 

Answer 1

Hello Cass.

 

Since the problem states no less than 80, we need to use the "greater than or equal to" symbol >=.  Ok, this problem must also have certain constraints.  On most tests that you take, there is a maximum number of points. It could be 100% , 0r may be more with an extra credit question.  But the symbol >= implies that you can get 1000, 10000000 on the test. 

 

So, after preaching a little, lets get back to the problem.  I am going to use x to represent the 3rd test.  You want an average of at least 80.  So the number of combine points that you are going to need are at least 240.  Why??  Well, you are taking the average.  And to take the average, you add all your points and divide by how many tests you take. 240/3= 80

 

So, the set up algebraically will be

 

[75+81+x]/3 = 80            I will change the sign to an inequality later on.

[75+81+x]    = 240           I multiplied both sides by 3.  If I do that, the denominator on the left will drop.

156+x          = 240            Subtract 155 from both sides

-156             = -156         

       x=84       

 So, the grade must be at least 84.  x>= 84.  Don't forget the constraint that I told you about.

 

I hope this helps out and thanks for posting.

 

D.Y. Taylor

don't forget to rate me :)

Answer 2

(75+81+x)/3 > 80  this shows us the average of the 3 grades must be greater than or equal to 80

[(75 + 81 + x)/3]*3 > 80 * 3  to eliminate the fraction, we multiply both sides by 3

156 + x > 240  we then simplify, or perform the operations on both sides of the inequality

156 -156 + x >  240 - 156  subtract both sides by 156 to get x alone

x > 84 solution says that the student must receive a grade of 84 or higher to have an average of 80 or better for the marking period