SOLUTION: Donna has scored 70 , 72 very quicky , 69 , 75 , and 65 on her previous five tests. What score does she need on her next test so that her average (mean) is 70 ?

Question 1090561: Donna has scored
70
,
72 very quicky
,
69
,
75
, and
65
on her previous five tests. What score does she need on her next test so that her average (mean) is
70
?
Found 2 solutions by Tatiana_Stebko, greenestamps:
Answer by Tatiana_Stebko(1539) (Show Source): You can put this solution on YOUR website!
Multiply both sides by 6

Donna needs to score 69 on her next test
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

If you are working a problem involving averages where the numbers are close together, often a fast way to get to the answer is to compare the individual numbers to the average. The idea is that if you have an average of x and one number is x-3, then there must be a number x+3 to balance things out.

We can use this method in your example to find the answer very quickly. One of the current five scores is exactly the desired average; and the two scores of 75 and 65 balance each other out. The remaining scores are 72 (2 above the desired average) and 69 (1 below the desired average).

So the student's "balance" going into the 6th test is +1; that means she needs to get a score 1 below the desired average in order to get the exact desired average. So the score she needs to get an average of exactly 70 is 70-1=69.

More realistically, if she needs to get an average of 70 OR MORE to pass, then she needs to get 69 OR HIGHER on the 6th test.
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