Going into the final exam which will count as two-thirds of the final grade, Mike has test scores of 86,80,84,and 90. What score does he need on the final to earn an average score of 80?
Is this right:
(86+80+84+90)/4 = 80
2/3x(85)= 80
or ((86+80+84+90+(2/3x))/5 = 80
the mean of the four test scores is worth 1/3 of his grade while his final is worth 2/3 of his grade
here's how to set it up:
(1/3)[(86+80+84+90)/4]+(2/3)x=80
To find out the score that Mike needs on the final exam to earn an average score of 80, you can use the weighted average formula.
First, let's calculate Mike's current average score:
(86 + 80 + 84 + 90)/4 = 85
His current average score is 85.
Now, let's set up the equation to find out what score he needs on the final exam:
(2/3) * x + (1/3) * 85 = 80
This equation takes into consideration that the final exam counts as two-thirds of the final grade, and the average of the previous four tests counts as one-third.
Now, we can simplify the equation:
(2/3) * x + (1/3) * 85 = 80
(2/3) * x + 85/3 = 80
Multiply both sides of the equation by 3 to get rid of the fraction:
2x + 85 = 240
Subtract 85 from both sides:
2x = 155
Divide both sides by 2:
x = 77.5
Therefore, Mike needs to score a 77.5 on the final exam to earn an average score of 80.