Her quiz scores so far are: 92, 95, 87, 89, and 100. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 93?

Question

Please show work&how to solve word problem. Thanks!

Answer 1

first find the total number of points for a mean of 93 in six scores

6*93=558

92+95+87+89+100+n=558 where n=the sixth quiz score

463+n=558

n=558-463

n=95 is needed on the sixth quiz

here's another way to look at the problem...

a mean of 93 for six scores is the same as getting a 93 on each of the six scores

compare each of her scores with the mean of 93 that she wants

92 (-1)

95 (+2)

87 (-6)

89 (-4)

100 (+7)

add the plus and minuses: (-1)+(+2)+(-6)+(-4)+(+7)=-2

she is 2 points (-2) below her 93 already before the next quiz

she has to make up 2 points (get 2 extra points) on her next quiz

getting a 93 won't do it, she'll still be 2 points behind

she has to get a 95 on her next quiz (93 for the mean of 93 and the 2 points that she's behind)

 

Answer 2

The mean is the sum of the averages over the number of objects.

Let x=6th quiz score.

(92+95+87+89+100+x)/6=93

(463+x)/6=93

463+x=93*6=558

463+x=558

x=95

Answer 3

Hi Sophie--

 

If the average (mean) of 6 scores is 93, that means that all 6 scores added together will 93 x 6, which is 558.

 

So you need to add the 5 scores you have, and then subtract that total from 558 to find the missing score.

 

Hope this hint helps, but post back if you need more!

 

Cheers,

 

Matt in NY

Answer 4

Hi Sophie, 

 

To find an arithmetic mean (also known as as average), you want to add up all of the numbers, and then divide by the number of numbers. 

You have 5 quiz grades that you know, plus one more that you don't know, making 6 the "number of numbers". 

You know that if you divide the total of all of the scores by 6, you'll get the average, 93 in this case, so you can set up an equation:

(add up the six quiz scores) / (# of quiz scores) = (arithmetic mean, aka average)

(add up the six quiz scores) / (6) = (93)

 

To add up the quiz scores, you've got: 92 + 95 + 87 + 89 + 100 + ???. Since this is algebra, you should pick a letter (a variable) to represent the score you don't know yet, x is a common choice. 

(add up the six quiz scores) = 92 + 95 + 87 + 89 + 100 + x

So your equation becomes: 

(92 + 95 + 87 + 89 + 100 + x) / (6) = (93)

 

Can you solve it from there?