Joe's test grades in History class are: 92%, 89%, 85%, 89%, and 90. The semester final will count as two tests. Joe needs to get a grade of 90% or higher for the semester to get an A. What is the minimum score Joe can get on the final test and average 90%?

- AndrewKaiser333

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- mathstudent55

How do you find the average grade of several grades?

- AndrewKaiser333

can you look it up i am stumped i was gone from school for several days due to the death of my mom

- AndrewKaiser333

I tried and i found nothing i am not sure what you look for first

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## More answers

- mathstudent55

To find the average of several grades, add up all the grades, and divide by the number of grades.

- AndrewKaiser333

ok can you start the equation?

- mathstudent55

You are given these test grades:
92, 89, 85, 89, 90
He will take a final exam and get one more grade that counts like two tests.
Since we don't know what his final exam grade is, we call it x.

- mathstudent55

That means the sum off all the grades will be:
\(92+ 89+ 85+ 89+ 90 +x + x\)
Ok so far?

- AndrewKaiser333

ok

- mathstudent55

To find the average, you divide the sum of the grades by the number of grades.
There are 7 grades altogether, so to find the average, we divide the sum by 7.
\(\dfrac{92+ 89+ 85+ 89+ 90 +x + x}{7}\)
Ok?

- AndrewKaiser333

k

- mathstudent55

We want the average to be 90 or more, so we now set it up as an inequality:
\(\dfrac{92+ 89+ 85+ 89+ 90 +x + x}{7} \ge 90\)

- mathstudent55

Now we need to solve the inequality for x.

- AndrewKaiser333

k

- mathstudent55

First, add all the numbers on the numerator of the fraction.
Also, what is x + x = ?

- AndrewKaiser333

\[\frac{ 445+2x }{ 7 }\

- AndrewKaiser333

\[\frac{ 445+2x }{ 7 }\]

- AndrewKaiser333

yes?

- mathstudent55

Great, so now we have this:
\(\dfrac{445 +2x}{7} \ge 90\)

- AndrewKaiser333

now x7

- mathstudent55

Correct.
Now multiply both sides by 7 to get rid of the denominator of 7.
\(7 \times \dfrac{445 +2x}{7} \ge 7 \times 90\)

- AndrewKaiser333

630

- AndrewKaiser333

445+2x >630

- AndrewKaiser333

-445

- AndrewKaiser333

2x>185

- mathstudent55

\(\cancel{7} \times \dfrac{445 +2x}{\cancel{7}~1} \ge 630\)
\(445 + 2x \ge 630\)
Now subtract 445 from both sides.

- AndrewKaiser333

/2

- mathstudent55

Correct.
Now divide both sides by 2.

- AndrewKaiser333

92.5>x

- mathstudent55

No. Be careful. Don't switch sides.

- AndrewKaiser333

oops

- AndrewKaiser333

how is it done then

- AndrewKaiser333

x>92.5

- mathstudent55

We had
\(2x \ge 185\)
Divide both sides by 2:
\(\dfrac{2x}{2} \ge \dfrac{185}{2}\)
We get:
\(x \ge 92.5\)

- AndrewKaiser333

ok

- mathstudent55

Correct, but remember it's "greater than or equal", not just plain "greater than."

- AndrewKaiser333

thanks i see now

- AndrewKaiser333

yes i know

- AndrewKaiser333

my keys just won't let me click to do it the way you did it

- AndrewKaiser333

it stopped working for some reason

- mathstudent55

Since the answer is
\(x \ge 92.5\)
That means as long as he gets at least 92.5% on the semester exam, he will have an 90% average, meaning he gets an A grade.

- mathstudent55

You're welcome.

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