I am trying to convert this problem from decimals to whole numbers and solve
it. But everytime I do I get this answer instead of 8 
Equation 0.2(s+0.2)+0.5(s-0.4)=5.44 
my work converting decimals to whole numbers (multiply by 100)
20s+400+50s-2000=544
70s-1600=544 (544+1600=2144)
70s=2144
s=30.628
The answer should be 8, what am I doing wrong here?

Your mistake is that you did not remove all the parentheses first,
before converting decimals to whole numbers.  Leave the decimals
until you have removed all parentheses.  Then convert to whole
numbers

 0.2(s + 0.2) + 0.5(s - 0.4) = 5.44
  0.2s + 0.04 + 0.5s - 0.2 = 5.44 
 
Now multiply through by 100 and you'll get s = 8

Edwin
AnlytcPhil@aol.com