SOLUTION: the math class has 4 exams. Each exam is out of 100 possible points. jackie got 67, 84, and 78. jackie wants to get at least a B.for the class, what score should she get on her las

Question 1086775: the math class has 4 exams. Each exam is out of 100 possible points. jackie got 67, 84, and 78. jackie wants to get at least a B.for the class, what score should she get on her last exam
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Exam Scores = {67,84,7,x} where x is a real number and
Sum of the scores = S = 67+84+78+x = 229+x
sample size = n = 4
Average = A = (sum of scores)/(sample size) = S/n = (229+x)/4

We want the average to be a B or higher. I'm assuming the grade "B" corresponds to a score of 80, which you could argue is a B- but I'm going to ignore the plus/minus for the letter grades.

So,
A > 80
(229+x)/4 > 80
4*(229+x)/4 > 4*80
229+x > 320
229+x-229 > 320-229
x > 91
So you need to get a score of 91 to get an overall average of 80
If you score higher than 91, then the average will be larger than 80

If you place a B grade at something like 85, then
A > 80
(229+x)/4 > 85
4*(229+x)/4 > 4*85
229+x > 340
229+x-229 > 340-229
x > 111
which is impossible to accomplish (x maxes out at 100)

You're probably wondering: "What is the highest average possible?". That happens when x = 100. Let's plug that into the equation below to find A
A = (229+x)/4
A = (229+100)/4
A = 82.25

So the best average possible is 82.25% or 82% if you round to the nearest whole percent.
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