Anumber is increased by 50 percent, then the resulting number is decreased by 40 percent. what is the original number if the final number is eight less than the original? ** show all work! **

With x as the original number, we can create an equation starting at the beginning of the problem and working toward the end in steps.
The first information we are given is that the original number was increased by 50 percent.  Keeping in mind that if we are increasing by a percentage we add the percentage to one and then multiply, our first alteration can be shown like this:
(x*(1+.5))=r
Then we are told the resulting number, r, is decreased by 40 percent.  Again, remember that to decrease by a percentage, we subtract from 1 and Multiply.  Expanding on our first equation, we get:
(x*1.5)*(1-.4)=final number
Finally getting to the really important question, we are asked to find the original number if the final number is eight less than the original.
Use the information underlined to create yet another small equation:
final number=x-8
We the8n plug this into our main equation:
(x*1.5)*(0.6)=x-8
Then 0we just follow the order of operations:
(x*1.5)*(0.6)=x-8
1.5x*0.6=x-8
(0.6*1.5)x=x-8
.9x=x-8
9x-x=x-x-8 Subtract x from both sides.
-.1x=-8 
.1x=8 The negatives cancel each other out.
.1x*10=8*10 We want to know what x is when it is whole, not a fraction of x.
x=80