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%?

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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%?

Mathematics
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How do you find the average grade of several grades?
can you look it up i am stumped i was gone from school for several days due to the death of my mom
I tried and i found nothing i am not sure what you look for first

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To find the average of several grades, add up all the grades, and divide by the number of grades.
ok can you start the equation?
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.
That means the sum off all the grades will be: \(92+ 89+ 85+ 89+ 90 +x + x\) Ok so far?
ok
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?
k
We want the average to be 90 or more, so we now set it up as an inequality: \(\dfrac{92+ 89+ 85+ 89+ 90 +x + x}{7} \ge 90\)
Now we need to solve the inequality for x.
k
First, add all the numbers on the numerator of the fraction. Also, what is x + x = ?
\[\frac{ 445+2x }{ 7 }\
\[\frac{ 445+2x }{ 7 }\]
yes?
Great, so now we have this: \(\dfrac{445 +2x}{7} \ge 90\)
now x7
Correct. Now multiply both sides by 7 to get rid of the denominator of 7. \(7 \times \dfrac{445 +2x}{7} \ge 7 \times 90\)
630
445+2x >630
-445
2x>185
\(\cancel{7} \times \dfrac{445 +2x}{\cancel{7}~1} \ge 630\) \(445 + 2x \ge 630\) Now subtract 445 from both sides.
/2
Correct. Now divide both sides by 2.
92.5>x
No. Be careful. Don't switch sides.
oops
how is it done then
x>92.5
We had \(2x \ge 185\) Divide both sides by 2: \(\dfrac{2x}{2} \ge \dfrac{185}{2}\) We get: \(x \ge 92.5\)
ok
Correct, but remember it's "greater than or equal", not just plain "greater than."
thanks i see now
yes i know
my keys just won't let me click to do it the way you did it
it stopped working for some reason
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.
You're welcome.

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