deirdre is a member of a very small but high class organization called algebra lovers anonymous. She paid $10 in dues for each of her first 3 years as a member and $2 in dues each year after that. If deirdre has paid a total of $38 in dues, for how many years has she paid $2 in dues?
Let's say Deirdre paid $2 in dues for x years.
She paid $10 in dues for each of her first 3 years, so she paid 3*$10 = $<<3*10=30>>30 in dues for the first 3 years.
Since she has paid a total of $38 in dues, the total amount she paid for $2 in dues is $38-$30 = $<<38-30=8>>8.
The number of years Deirdre paid $2 in dues is $8/$2 = <<8/2=4>>4 years. Answer: \boxed{4}.