Question

What’s the range of grades on the fifth exam that results in earning a B is _. If the highest grade is 100 then _ .

Answer 1

73-100

Explanation:

Steve has a pretty lenient grading system! (Usually 85-93 is a B.)

He needs at LEAST an 80 , so the average of his five scores must meet this

(71+76+88+92+x) / 5 = 80

solve for x = 73

If he scores less than a 90 average , he will still get a B

(71+ 76 + 88+92 +x) / 5 < 90 shows x < 123 ( which he cannot score)

so the range of scores on fifth test to get a final grade B is 73 - 100 .

Answer 2

Let x be the grade of the last exam, then the average is:

`(71+76+88+92+x)/(5)=(x+327)/(5)`

now, to get a B we need this to be greater or equal than 80 and less than 90, that is:

`80\leq(x+327)/(5)<90`

Solving for x we have:

`\begin{gathered} 80\leq(x+327)/(5)<90 \\ 5\cdot80\leq x+327<5\cdot90 \\ 400\leq x+327<450 \\ 400-327\leq x<450-327 \\ 73\leq x<123 \end{gathered}`

Therefore the range of grades on the fifth exam that results in earnings a B is

`73\leq x<123`

If the highest grade is 100, then

`73\leq x\leq100`