Question 878712
MENTAL MATH:
I would average the two numbers in my head, and come up with {{{highlight(96)}}} .
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+y}}} .
Since the number is that much less than 108 the number is
{{{x=108-y}}} .
So we write the system of equations
{{{system(x=84+y,x=108-y)}}}
and we solve it by institution, substituting the expression {{{108-y}}} for {{{x}} in {{{x=84+y}}} , to get
{{{108-y=84+y}}} .
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+y}}}-->{{{108=84+y+y}}}-->{{{108=84+2y}}}-->{{{108-84=2y}}}-->{{{24=2y}}}-->{{{24/2=y}}}-->{{{highlight(y=12)}}}
{{{system(x=84+y,y=12)}}} ---> {{{x=84+12}}} ---> {{{highlight(x=96)}}}
 
There are many other ways to solve it.