Question 1151997: The average of two numbers is 11.the difference between them is 4,find the number
Found 5 solutions by MathLover1, MathTherapy, Alan3354, ikleyn, greenestamps:
Answer by MathLover1(20850)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
The average of two numbers is 11.the difference between them is 4,find the number
Let larger be L
Then smaller = L - 4
With average being 11, we get: 
2L - 4 = 22 ------ Cross-multiplying
2L = 26
L, or larger = 
You should be able to find the smaller, if both are needed!
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The average of two numbers is 11.
--> the sum is 22.
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the difference between them is 4, find the number
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a + b = 22
a - b = 4
------------------- Add
Answer by ikleyn(52802)  (Show Source):
You can put this solution on YOUR website! .
When you solve similar problems 10 - 20 times, you will empirically come to this simple rule:
The numbers in such problems are equal to the average PLUS / MINUS half of the difference between them.
Concretely, in this problem the numbers are
11 +/-  = 11 +/- 2, i.e.
one number is 11+2 = 13, while the other number is 11-2 = 9.
ANSWER. The numbers are 9 and 13.
And it is absolutely correct rule, allowing you solve such problems mentally in the future.
MEMORIZE and LEARN it once and for all.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
You have received three responses showing different algebraic solution methods, or the beginnings of algebraic solution methods.
All three are fine... if an algebraic solution is required.
If an algebraic solution is not required, then use your common sense to solve the problem quickly by the method shown by tutor @ikleyn.
Here is a little more on her method, in case it is not clear to you.
(1) If you know the average of two numbers is x and the two numbers are the same, then obviously the two numbers are x and x.
(2) If you know the average of two numbers is x and the difference between the two numbers is 2, then take the x and x from example (1) and add 1 to one of them and subtract 1 from the other; the two numbers are x+1 and x-1. The average is then still the same, but now the numbers differ by 2.
So if you know the average is x and the two numbers differ by 10, then you know one number is 5 more than x and the other is 5 less than x; they are x+5 and x-5.
Applying the principle to this particular problem, with an average of 11 and a difference of 4, you get what tutor @ikleyn says for the two numbers: 11+2=13 and 11-2=9.
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