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Question 60613: The sum of two numbers is 33. Their difference is 9. What are the two numbers? This is how I solved am I right if not what did I do wrong?
x+9=33
y-9=33
24+9=33
42-9=33
Found 2 solutions by consc198, ikleyn:
Answer by consc198(59)   (Show Source):
Answer by ikleyn(53874)  (Show Source):
You can put this solution on YOUR website! .
The sum of two numbers is 33. Their difference is 9. What are the two numbers?
This is how I solved am I right if not what did I do wrong?
x+9=33
y-9=33
24+9=33
42-9=33
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The answer by @consc198, "Yes this is correct ", is WRONG.
For a correct solution see what follows.
Let the numbers be x and y: x the greater, y the smaller.
From the problem, you have these two equations
x + y = 33,
x - y = 9.
To find x, add the equations. You will get
2x = 33 + 9, or 2x = 42, x = 42/2 = 21.
To find y, from the first equation subtract the second equation. You will get
y - (-y) = 33 - 9, or 2y = 24, y = 24/2 = 12.
ANSWER. The numbers are 21 and 12.
Solved correctly.
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For this problem, and for many other similar problems, there is a shortcut,
which allows to get the answer MENTALLY and quickly:
- - - one number is half-the-sum, while the other number is half-the difference of the given numbers.
In our case, one number is  =  = 21; the other number is  =  = 12.
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