SOLUTION: A number is such that it is as much greater than 84 as it is less than 108. find it

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Question 878712: A number is such that it is as much greater than 84 as it is less than 108. find it
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
MENTAL MATH:
I would average the two numbers in my head, and come up with highlight%2896%29 .
In my head I really average their differences to 100.
I see 84 as 84 - 100 = -16, and I see 108 as 8.
I add -16+8=-8, and divide by 2 to find the average as -4.
That means that the number is -4 + 100 = 96.

SYSTEM OF EQUATIONS:
x= the number
y= how much greater than 84 the number is
Since the number is that much greater than 84 the number is
x=84%2By .
Since the number is that much less than 108 the number is
x=108-y .
So we write the system of equations
system%28x=84%2By%2Cx=108-y%29
and we solve it by institution, substituting the expression 108-y for x%7D%7D+in+%7B%7B%7Bx=84%2By , to get
108-y=84%2By .
We solve for y , and then we plug the value found for y into either of the original equations yo find x .
108-y=84%2By-->108=84%2By%2By-->108=84%2B2y-->108-84=2y-->24=2y-->24%2F2=y-->highlight%28y=12%29
system%28x=84%2By%2Cy=12%29 ---> x=84%2B12 ---> highlight%28x=96%29

There are many other ways to solve it.