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%, 65%, 89%, and 80%. What range of grades on the fifth test would him a B in the course? ( Assume that 100% is the highest grade possible.)

Enter the range of grades necessary for Devon to earn a b average.

__% < x < 100%
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Answer 1

• 90% ≤ x ≤ 100%

Explanation:

Test results are:

• 76, 65, 89, 80 and x.

The average of 5 tests should be:

• 80 ≤ average < 90, to get a B.

The average is:

• (76 + 65 + 89 + 80 + x)/5 =
• (310 + x)/5

Plug it into inequality:

• 80 ≤ (310 + x)/5 < 90 Multiply by 5
• 400 ≤ 310 + x < 450 Subtract 310
• 90 ≤ x < 140

But the maximum possible result from one test is 100%, considering this top score Devon must get:

• 90% ≤ x ≤ 100%