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A student must have an average​ (the mean) on five tests that is greater than or equal to​ 80% but less than​ 90% to receive a final grade of B.​ Devon's grades on the first four tests were 76​%, 61​%, 90​%, and 77​%. What range of grades on the fifth test would give him a B in the​ course? (Assume that​ 100% is the highest grade​ possible.)

Question

A student must have an average​ (the mean) on five tests that is greater than or equal to​ 80% but less than​ 90% to receive a final grade of B.​ Devon's grades on the first four tests were 76​%, 61​%, 90​%, and 77​%. What range of grades on the fifth test would give him a B in the​ course? (Assume that​ 100% is the highest grade​ possible.)

check_circleAnswer
Step 1

Let x be the range of grade in fifth test.

Step 2

Then according to given conditions, we get

76+61 90 77 + x
80
sum of all the observations
90
average-
number of observations
5
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Image Transcriptionclose

76+61 90 77 + x 80 sum of all the observations 90 average- number of observations 5

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Step 3

Solving the above ineq...

304+x90
80
5
multiplying by 5, we get
400 304 x450
Subtracting by 304, we get
96 x<146
help_outline

Image Transcriptionclose

304+x90 80 5 multiplying by 5, we get 400 304 x450 Subtracting by 304, we get 96 x<146

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Tagged in

Math

Algebra

Equations and In-equations

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