## AndrewKaiser333 one year ago 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%?

1. mathstudent55

2. AndrewKaiser333

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

3. AndrewKaiser333

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

4. mathstudent55

5. AndrewKaiser333

ok can you start the equation?

6. 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.

7. mathstudent55

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

8. AndrewKaiser333

ok

9. 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?

10. AndrewKaiser333

k

11. mathstudent55

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

12. mathstudent55

Now we need to solve the inequality for x.

13. AndrewKaiser333

k

14. mathstudent55

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

15. AndrewKaiser333

$\frac{ 445+2x }{ 7 }\ 16. AndrewKaiser333 \[\frac{ 445+2x }{ 7 }$

17. AndrewKaiser333

yes?

18. mathstudent55

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

19. AndrewKaiser333

now x7

20. mathstudent55

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

21. AndrewKaiser333

630

22. AndrewKaiser333

445+2x >630

23. AndrewKaiser333

-445

24. AndrewKaiser333

2x>185

25. mathstudent55

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

26. AndrewKaiser333

/2

27. mathstudent55

Correct. Now divide both sides by 2.

28. AndrewKaiser333

92.5>x

29. mathstudent55

No. Be careful. Don't switch sides.

30. AndrewKaiser333

oops

31. AndrewKaiser333

how is it done then

32. AndrewKaiser333

x>92.5

33. mathstudent55

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

34. AndrewKaiser333

ok

35. mathstudent55

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

36. AndrewKaiser333

thanks i see now

37. AndrewKaiser333

yes i know

38. AndrewKaiser333

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

39. AndrewKaiser333

it stopped working for some reason

40. 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.

41. mathstudent55

You're welcome.