SOLUTION: A student scores 75, 86, and 72 on three 100-point exams. If the final is worth 150 points, find the range of final exam score,S, that gives the student an overall percentage of 80

Question 257556: A student scores 75, 86, and 72 on three 100-point exams. If the final is worth 150 points, find the range of final exam score,S, that gives the student an overall percentage of 80% or higher. This is as far as I could get.
x= final exam score
S(x)= final average if final exam score is x
Not sure where to go from here. None of the answers I come up with make sense. Please help.
Found 2 solutions by rfer, stanbon:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
since these scores are all percentages, I don't think the 150 is an issue.
(75+86+72+x)/4=80
(233+x)/4=80
233+x=320
x=87% on final
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A student scores 75, 86, and 72 on three 100-point exams. If the final is worth 150 points, find the range of final exam score,S, that gives the student an overall percentage of 80% or higher.
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Total # of possible points = 3*100+150 = 450
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80% of 450 = 360
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The student has 75+86+72 = 233 points from the 1st 3 exams.
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Ans: 360-233 <= S <= 150
127 <= S <= 150
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Cheers,
Stan H.
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