SOLUTION: Frank got scores of 75, 83, and 79 on his first three tests. What score does he need to make on his next test to have an average of 80?

Question 123207: Frank got scores of 75, 83, and 79 on his first three tests. What score does he need to make on his next test to have an average of 80?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
When Frank completes his next test, he will have done 4 tests. If he is to average 80 on these
4 tests, he will need to score a total of 320 points on the 4 tests ... because 320 total
points divided by 4 will result in an average of 80.
.
On the 3 tests he has completed already, Frank has scored 75 + 83 + 79 = 237 points. His
next test has to add enough points to take the total to 320 points. So, on his next test
Frank has to score 320 minus 237 points, and that means he must get 83 points on his next test.
.
Another tricky way to work this problem is to look at his present scores as they compare to
the 80 average he wants after his next test. On his first test he got a 75. That is 5 points
below his desired average. On his second test he got and 83 and that is 3 points above his
desired average. On his third test he got 79 and this is 1 point below his desired average.
That means relative to his desired average of 80 he is a total of 3 points below what he needs.
This comes from -5 +3 -1 = -3 where the minus signs indicate the number of points below
the desired average and the + sign indicates more than the desired average. Since after 3
tests he is 3 points below the desired average, on the next test he must score 3 points more than
the desired average to counteract the shortfall. Therefore, he must score 83 points. This
means that relative to the desired average of 80 on the 4 tests on each of the 4 tests he will
have scored -5 +3 -1 +3 = 0, so he will be exactly on the 80 average (80 + 0).
.
Hope both methods make sense to you and help you to understand the problem a little better.
.
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