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Question 1174367: The difference between the two numbers is 7.Their sum is 17.Find the numbers.Find the solution (x,y)
Found 2 solutions by ewatrrr, greenestamps:
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
The difference between the two numbers is 7.Their sum is 17
y - x = 7
y + x = 17
2y = 24
y = 12 and x = 5
P(5,12) is the solution for this System of Equations
Wish You the Best in your Studies.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
There are many different kinds of problems where the basic task is to solve a system that says the sum of two numbers is A and the difference of the two numbers is B.
If a formal algebraic solution is required, then something like what the other tutor showed is fine.
But if the speed of solving the problem is important and a formal algebraic solution is not required (as in a timed math competition), there is a quick and easy informal way to solve this type of problem.
Look at it this way:
There is a number somewhere on a number line.
If you add some number, you reach A; if you subtract the same number, you reach B.
You went equal distances in opposite directions from the starting point to reach A and B; that means the starting point is halfway between A and B. Mathematically, that means the starting point is the average of A and B.
So one of the two numbers you are looking for is the average of the sum and difference of the two numbers; then the second number is the difference between that average and either of the numbers.
That's a lot of words of explanation - but using the process is simple.
For this example, we have a difference of 7 and a sum of 17.
One of the numbers is the average of 7 and 17, which is (7+17)/2 = 12.
The other number is the difference between 7 and 12, or between 12 and 17, which is 5.
ANSWER: 12 and 5
A couple of other quick examples to see how easy this method is....
Sum 24 and difference 6 --> first number (24+6)/2 = 30/2 = 15; second number 24-15=9, or 15-6=9
Sum 37 and difference 29 --> first number (37+29)/2 = 33; second number 37-33=4, or 33-29=4
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