SOLUTION: If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable. 12, 18, 21, c, 13

Question 1195486: If the mean of the following numbers is 17, find the c value. Produce an algebraic solution. Guess and check is unacceptable.
12, 18, 21, c, 13
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

You finish! Edwin

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A typical algebraic solution....

(12+18+21+c+13)/5 = 17
12+18+21+c+13 = 85
64+c = 85
c = 21

That method for solving the problem is fine since the numbers are small, so adding the numbers is an easy task.

If the numbers are much larger but still close together, an often useful method for solving a problem like this is to compare each number to the desired mean, knowing that the "overs" and "unders" have to balance.

For this example, with the average being 17....
12: 5 under
18: 1 over
21: 4 over
13: 4 under

Note the first three numbers balance; overall the four scores are 4 under the desired average.

That means c must be 4 over the desired average. So

ANSWER: c = 17+4 = 21

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