Question

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%?

Answer 1

How do you find the average grade of several grades?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

ok can you start the equation?

Answer 6

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.

Answer 7

That means the sum off all the grades will be:

\(92+ 89+ 85+ 89+ 90 +x + x\)

Ok so far?

Answer 8

ok

Answer 9

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?

Answer 10

k

Answer 11

We want the average to be 90 or more, so we now set it up as an inequality:

\(\dfrac{92+ 89+ 85+ 89+ 90 +x + x}{7} \ge 90\)

Answer 12

Now we need to solve the inequality for x.

Answer 13

k

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

yes?

Answer 18

Great, so now we have this:

\(\dfrac{445 +2x}{7} \ge 90\)

Answer 19

now x7

Answer 20

Correct.

Now multiply both sides by 7 to get rid of the denominator of 7.

\(7 \times \dfrac{445 +2x}{7} \ge 7 \times 90\)

Answer 21

630

Answer 22

445+2x >630

Answer 23

-445

Answer 24

2x>185

Answer 25

\(\cancel{7} \times \dfrac{445 +2x}{\cancel{7}~1} \ge 630\)

\(445 + 2x \ge 630\)

Now subtract 445 from both sides.

Answer 26

/2

Answer 27

Correct.
Now divide both sides by 2.

Answer 28

92.5>x

Answer 29

No. Be careful. Don't switch sides.

Answer 30

oops

Answer 31

how is it done then

Answer 32

x>92.5

Answer 33

We had

\(2x \ge 185\)

Divide both sides by 2:

\(\dfrac{2x}{2} \ge \dfrac{185}{2}\)

We get:

\(x \ge 92.5\)

Answer 34

ok

Answer 35

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

Answer 36

thanks i see now

Answer 37

yes i know

Answer 38

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

Answer 39

it stopped working for some reason

Answer 40

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.

Answer 41

You're welcome.