Number Theory

We can rewrite this as$1000 \leq 47x + 3 \leq 2000$, which we can simplify

$997 \leq 47x \leq 1997$

$21\frac{10}{47}\leq x\leq 42\frac{23}{47}$

The only natural numbers that fit in that range are 22 through 42, and there are 21 numbers in that range.