my grade: test grades 86, 88; find grade needed on final for

[Bubbles28]

On two examinations, you have grades of 86 and 88. There is an optional final examination, which counts as one grade. You decide to take the final in order to get a course grade of A, meaning a final average of at least 90.

a.What must you get on the final to earn an A in the course?
b.By taking the final, if you do poorly, you might risk the B that you have in the course based on the first two exam grades. If your final average is less than 80, you will lose your B in the course. Describe the grades on the final that will cause this to happen.

 

[soroban]

Re: my grade

Hello, Bubbles28!

I must assume that you know how to average three grades.
. . Add them and divide by 3, right?

On two examinations, you have grades of 86 and 88.
There is an optional final examination, which counts as one grade.
You decide to take the final in order to get a course grade of A,
meaning a final average of at least 90.

a. What must you get on the final to earn an A in the course?

Let \(\displaystyle F\) = your final exam grade.

\(\displaystyle \text{Then you want: }\:\frac{86 + 88 + F}{3} \:\geq \:90\)

. . Multiply by 3: .\(\displaystyle 174 + F \:\geq \:270\)

. . Subtract 174: .\(\displaystyle F \:\geq \:96\)

You must get at least a 96 on the Final to get an "A".

b. By taking the final, if you do poorly, you might risk the B that you have
based on the first two exam grades.
If your final average is less than 80, you will lose your B in the course.
Describe the grades on the final that will cause this to happen.

\(\displaystyle \text{You will lose your "B" if: }\:\frac{174+F}{3} \:<\:80\)

. . Multiply by 3: .\(\displaystyle 174 + F \:<\:240\)

. . Subtract 174: .\(\displaystyle F \:<\:66\)

You will lose your "B" if your Final grade is 65 or less.