Gail needs to earn a B in her Geology class. Her current test scores are 89, 78, 77, and 85. Her final exam is worth 3 test scores. In order to earn a B, Gail's average must lie between 80 and 89 inclusive. What range of scores can Gail receive on the final exam to earn a B in the course? I don't know how to do inclusive compound inequalities, can someone walk me through the process?

Question

Gail needs to earn a B in her Geology class. Her current test scores are 89, 78, 77, and 85. Her final exam is worth 3 test scores. In order to earn a B, Gail's average must lie between 80 and 89 inclusive. What range of scores can Gail receive on the final exam to earn a B in the course? I don't know how to do inclusive compound inequalities, can someone walk me through the process?

Answer 1

I need someone to reply quick, Please! I didn't have time to study and I don't want to get a bad grade. This is the last question can someone please help me.

Answer 2

Thanks for the reply, Reiny! I think I know what to do, but If I don't understand then I'll ask. I wasn't asking for sympathy. I didn't have time because I just gave birth to twins and still have assignments to do.

Answer 3

To find the range of scores Gail can receive on the final exam to earn a B in the course, we need to work with compound inequalities. We know that Gail's average must lie between 80 and 89 inclusive, which means it needs to be greater than or equal to 80 and less than or equal to 89.

First, let's calculate Gail's current average test score. To do this, we add up her current test scores and divide by the total number of test scores:
(89 + 78 + 77 + 85) / 4 = 329 / 4 = 82.25

So, Gail's current average is 82.25. Now, let's consider the final exam. We know that the final exam is worth 3 test scores, so we need to calculate the weighted average.

To find the range of scores Gail can receive on the final exam, we will consider the highest and lowest possible scores she can achieve.

To find the highest possible score, we assume that Gail's current average is at its lowest (80), and then we add three perfect test scores (100 each):
(82.25 * 4 + 100 * 3) / 7 = 507.75 / 7 = 72.54

So, the highest possible weighted average Gail can achieve is 72.54.

To find the lowest possible score, we assume that Gail's current average is at its highest (89), and then we add three scores of 0 (minimum score on each test):
(89 * 4 + 0 * 3) / 7 = 356 / 7 = 50.86

So, the lowest possible weighted average Gail can achieve is 50.86.

Therefore, to earn a B in the course, Gail's weighted average score on the final exam needs to be between 50.86 and 72.54 inclusive.

Answer 4

consider her final exam as 3x or x+x+x

solve:
80 ≤ (89+78+77+85+x+x+x)/7 ≤ 89

(If you did not take the time to study, you must accept the consequences for that. You will not get any sympathy from me)