AndrewKaiser333
  • AndrewKaiser333
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathstudent55
  • mathstudent55
How do you find the average grade of several grades?
AndrewKaiser333
  • 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
  • AndrewKaiser333
I tried and i found nothing i am not sure what you look for first

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More answers

mathstudent55
  • mathstudent55
To find the average of several grades, add up all the grades, and divide by the number of grades.
AndrewKaiser333
  • AndrewKaiser333
ok can you start the equation?
mathstudent55
  • 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
  • mathstudent55
That means the sum off all the grades will be: \(92+ 89+ 85+ 89+ 90 +x + x\) Ok so far?
AndrewKaiser333
  • AndrewKaiser333
ok
mathstudent55
  • 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
  • AndrewKaiser333
k
mathstudent55
  • 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
  • mathstudent55
Now we need to solve the inequality for x.
AndrewKaiser333
  • AndrewKaiser333
k
mathstudent55
  • mathstudent55
First, add all the numbers on the numerator of the fraction. Also, what is x + x = ?
AndrewKaiser333
  • AndrewKaiser333
\[\frac{ 445+2x }{ 7 }\
AndrewKaiser333
  • AndrewKaiser333
\[\frac{ 445+2x }{ 7 }\]
AndrewKaiser333
  • AndrewKaiser333
yes?
mathstudent55
  • mathstudent55
Great, so now we have this: \(\dfrac{445 +2x}{7} \ge 90\)
AndrewKaiser333
  • AndrewKaiser333
now x7
mathstudent55
  • 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
  • AndrewKaiser333
630
AndrewKaiser333
  • AndrewKaiser333
445+2x >630
AndrewKaiser333
  • AndrewKaiser333
-445
AndrewKaiser333
  • AndrewKaiser333
2x>185
mathstudent55
  • mathstudent55
\(\cancel{7} \times \dfrac{445 +2x}{\cancel{7}~1} \ge 630\) \(445 + 2x \ge 630\) Now subtract 445 from both sides.
AndrewKaiser333
  • AndrewKaiser333
/2
mathstudent55
  • mathstudent55
Correct. Now divide both sides by 2.
AndrewKaiser333
  • AndrewKaiser333
92.5>x
mathstudent55
  • mathstudent55
No. Be careful. Don't switch sides.
AndrewKaiser333
  • AndrewKaiser333
oops
AndrewKaiser333
  • AndrewKaiser333
how is it done then
AndrewKaiser333
  • AndrewKaiser333
x>92.5
mathstudent55
  • 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
  • AndrewKaiser333
ok
mathstudent55
  • mathstudent55
Correct, but remember it's "greater than or equal", not just plain "greater than."
AndrewKaiser333
  • AndrewKaiser333
thanks i see now
AndrewKaiser333
  • AndrewKaiser333
yes i know
AndrewKaiser333
  • AndrewKaiser333
my keys just won't let me click to do it the way you did it
AndrewKaiser333
  • AndrewKaiser333
it stopped working for some reason
mathstudent55
  • 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
  • mathstudent55
You're welcome.

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