SOLUTION: the average of the first three numbers is double of the fourth number. if the average of all the four numbers is 12.find the fourth number?

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Question 825711: the average of the first three numbers is double of the fourth number. if the average of all the four numbers is 12.find the fourth number?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the four numbers a, b, c and d. Then "the average of the first three numbers is double of the fourth number" translates into:
%28a%2Bb%2Bc%29%2F3=2d
Multiplying both sides by 3 we get:
a%2Bb%2Bc=6d

"the average of all the four numbers is 12" translates into:
%28a%2Bb%2Bc%2Bd%29%2F4=+12
Multiplying each side by 4 we get:
a%2Bb%2Bc%2Bd=+48
From the earlier equation we found that a+b+c = 6d. Substituting this into the second equation we get:
%286d%29%2Bd=+48
Simplifying we get:
7d+=+48
Dividing by 7:
d+=+48%2F7
Since "d" was the fourth number and since that is what we were asked to find, this is the answer to the problem.