What is the average quiz score? HELP PLEASE! :)

Question

Micah scores 80 on his tenth quiz, increasing his quiz average by 2 points. What is his new quiz average?

Answer 1

To find an average, you add all the scores and divide by the number of scores. In this problem you don't know the total of the first 9 quizzes, or the original average. There are two situations, however, so we can solve for the two unknowns.

 

Let T be the total score on the first 9 quizzes.

Let A be the average of the first 9 quizzes.

 

T/9 = A

 

The total score of all 10 quizzes is T + 80

The average of all 10 quizzes is A + 2

 

(T+80)/10 = A + 2

 

To make solving easier, multiply both sides of the first equation by 9, and both sides of the second by 10

9*(T/9) = 9*A

T = 9A

 

10*(T+80)/10 = 10(A+2)

T + 80 = 10A + 20    -- then subtract 20 from both sides

T + 60 = 10A

 

Your system of two equations is

T = 9A

T + 60 = 10A

 

You can solve this fairly easily either by substituting 9A in for T in the second equation, or by subtracting the two equations to eliminate T.

 

Don't forget what the question is asking for, the new average, which is A+2.

Answer 2

Micah has 9 tests. Whatever his average is, it's the same as having 9 scores all the same.

If someone has an average of 70 on 9 tests, it's the same as getting 70 on each one.

This said...

x=the old average

(9x+80)/10=x+2

9x+80=10(x+2)

9x+80=10x+20

80-20=10x-9x

60=x

His average was 60 and it went up 2 points to 62.

Answer 3

Piya, I hope I'm not too late to help.  Let's think about this.  The average is all the scores added together, divided by the number of test scores, right?

 

So, we have 9 scores that were added together and divided by 9 to get his old average.  If we take the new total and divide by 10, the average goes up 2 points.

 

We first need to realize that the first total of his quiz scores has to be a multiple of 9.  The second total has to be a multiple of 10, but 80 points higher than the first.  Since 80 is also a multiple of 10, then the old total also had to be a multiple of 10.  Make sense?

 

What's the LCM of 9 and 10?  90, so let's start there.  90/9 = 10.  90+80/10 = 170/10 = 17.  17 - 10 ≠ 2.

 

180/9 = 20.  260/10 = 26.  Getting closer.  

 

270/9 = 30.  350/10 = 35.  

 

You may see a pattern here.  The first average is going up by 10, while the second average is going down by 9.  The digits of the second average added together equal 8, and the difference goes down by 1 each time. 

 

40 and 44?  Nope

 

50 and 53? Closer still

 

60 and 62?  There ya go.

 

There is a way more complicated way to figure this out, but a little trial and error usually works.

 

Hope this helps!