1958 AHSME Problem 32

With 1000 a rancher is to buy steers at 25 each and cows at 26 each. If the number of steers s and the number of cows c$ are both positive integers, then:

\textbf{(A)}\ \text{this problem has no solution}\qquad\\ \textbf{(B)}\ \text{there are two solutions with }{s}\text{ exceeding }{c}\qquad \\ \textbf{(C)}\ \text{there are two solutions with }{c}\text{ exceeding }{s}\qquad \\ \textbf{(D)}\ \text{there is one solution with }{s}\text{ exceeding }{c}\qquad \\ \textbf{(E)}\ \text{there is one solution with }{c}\text{ exceeding }{s}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.