MathDB
Steers and Cows

Source:

June 13, 2009
modular arithmeticleast common multiplenumber theoryDiophantine equation

Problem Statement

With $1000 \$1000 a rancher is to buy steers at $25 \$25 each and cows at $26 \$26 each. If the number of steers s s and the number of cows c c are both positive integers, then: <spanclass=′latex−bold′>(A)</span> this problem has no solution<spanclass=′latex−bold′>(B)</span> there are two solutions with s exceeding c<spanclass=′latex−bold′>(C)</span> there are two solutions with c exceeding s<spanclass=′latex−bold′>(D)</span> there is one solution with s exceeding c<spanclass=′latex−bold′>(E)</span> there is one solution with c exceeding s <span class='latex-bold'>(A)</span>\ \text{this problem has no solution}\qquad\\ <span class='latex-bold'>(B)</span>\ \text{there are two solutions with }{s}\text{ exceeding }{c}\qquad \\ <span class='latex-bold'>(C)</span>\ \text{there are two solutions with }{c}\text{ exceeding }{s}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{there is one solution with }{s}\text{ exceeding }{c}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{there is one solution with }{c}\text{ exceeding }{s}
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