+826 How many numbers between $1000$ and $2000$ leave a remainder of $3$ when divided by $47?$
+135 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.
