This Quiz: 2 pts possibleHelpIn your class, you have scores of 85, 85, 78, and 80 on the first four of five tests. To get a grade of B, the average of the first five tests scores must be greater than orequal to 80 and less than 90a. Solve an inequality to find the least score you can get on the last test and still earn a B.b. What score do you need if the fifth test counts as two tests?a. The least score you need on the last test to get a Bis Nb. If the fifth test counts as two tests, the least score you need to get a Bis5/7

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AzmariahZ542516 AzmariahZ542516 · Answer 1 · 2022-10-31T02:18:04+01:00

(a).

Let us call the score on the fifth test a, then the average of the five tests is

[tex]\frac{85+85+78+80+a}{5}=\frac{328+a}{5}[/tex]

To get a grade of B, this average score must be greater than or equal to 80 and less than 90. In mathematical notation we can write this statement as

[tex]80\leq\frac{328+a}{5}<90[/tex]

Now, we need to solve the inequality for a. Solving for a gives

[tex]72\leq a<120[/tex]

Which is the range of scores required on the fifth test.

The least score of 72 ensures that you can earn a B.

(b)

If we count the fifth test as two tests then we have the inequality

[tex]80\leq\frac{328+2a}{6}<90[/tex]

Solving it gives us

[tex]76\leq a<106[/tex]

The least score that you need on the fifth and sixth test must be 76.