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Question 1118524: Half the sum of two numbers is 20 and twice the difference between the two numbers is 8.Find the numbers
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39630)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! Write an equation for each statment, simplify
:
Half the sum of two numbers is 20
 (a + b = 20
multiply both sides by 2
a + b = 40
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and twice the difference between the two numbers is 8.
2(a - b) = 8 Find the numbers
divide both sides by 2
a - b = 4
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Use elimination
a + b = 40
a - b = 4
------------Addition eliminates b, find a
2a = 44
a = 44/2
a = 22
Find b
22 + b = 40
b = 40 - 22
b = 18
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Half the sum of the two numbers is 20, so the sum of the two numbers is 40.
Twice the difference between the two numbers is 8, so the difference between them is 4.
Now you have the sum of the two numbers being 40 and the difference being 4. While an algebraic solution as shown by the other tutors is fine, you can find the answer with much less work using logical analysis and a bit of mental arithmetic.
When you know the sum of two numbers and the difference between those two numbers, one of the numbers is halfway between the sum and the difference, and the other is the difference between that first number and either the sum or the difference.
In words it sounds very confusing; but it is quite simple.
For your example, the sum is 40 and the difference is 4:
(1) One of the numbers is halfway between 40 and 4 -- i.e., the average of 40 and 4. (40+4)/2 = 22; one of the numbers is 22.
(2) The other number is the difference between either 40 and 22 (40-22=18) or the difference between 22 and 4 (22-4 = 18).
So the two numbers are 22 and 18.
It's even faster without all the words of explanation:
(40+4)/2 = 22; 22-4 = 18; the numbers are 22 and 18.
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