2001 AMC 12 Problem 7

Let $n$ tickets sell at full price $p$ dollars. Then $$np + (140 - n)\dfrac{p}{2} = 2001,$$ so $p(n + 140)$ $= 4002$ $= 2 \cdot 3 \cdot 23 \cdot 29.$ Since $0 \le n \le 140,$ we need a factor of $4002$ with $140 \le n + 140 \le 280.$ The only such factor is $174 = 2 \cdot 3 \cdot 29,$ giving $n = 34$ and $p = 23.$ The full-price tickets raise $34 \cdot 23 = 782$ dollars. Thus, the correct answer is A.