ceiling functionanalytic geometrygraphing linesslopefunctionalgebrasystem of equations
Problem Statement
Positive integers a, b, and c are chosen so that a<b<c, and the system of equations
2x\plus{}y\equal{}2003\text{ and }y\equal{}|x\minus{}a|\plus{}|x\minus{}b|\plus{}|x\minus{}c|
has exactly one solution. What is the minimum value of c?
<spanclass=′latex−bold′>(A)</span>668<spanclass=′latex−bold′>(B)</span>669<spanclass=′latex−bold′>(C)</span>1002<spanclass=′latex−bold′>(D)</span>2003<spanclass=′latex−bold′>(E)</span>2004