SOLUTION: the mean of ten positive numbers is 16. When another number is added the mean is 18. find the number

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Question 1115543: the mean of ten positive numbers is 16. When another number is added the mean is 18. find the number
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52879)   (Show Source):
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You are given = 16, which implies sum of ten = 10*16 = 160. You are also given = 18, which gives you 160+x = 11*18 = 198 ====> x = 198 - 160 = 38.

Solved.

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Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!

Here is an alternative method I like to use when working with means (averages) where the numbers are relatively simple numbers.

The individual numbers don't matter; since the mean of the original 10 numbers is 16, we can let each of them be equal to 16.

After the 11th number is added, the mean of all 11 numbers is 18.

Each of the 10 original numbers is 2 short of that mean; that means the sum of those original 10 numbers is 20 short of the total required to get the new mean of 18.

That means the 11th number, to balance the shortfall from the original 10 numbers, must be 20 MORE than the new mean.

So the 11th number is 18+20 = 38.