In melts, ring polymers assume more compact conformations compared to linear chains with the same degree of polymerization N-r, i.e. R-r similar to N-r(nu) with nu approximate to 0.4, where R-r is the radius of gyration. Upon gradually substituting some of the ring polymers with linear chains, the ring molecules swell. In the limit of infinite dilution, their size scales as R-r similar to N-r(0.5). We present a scaling argument based on the blob model to capture this transition. Ring-linear blends are modeled as a semidilute solution of ring polymers in a theta-solvent consisting of linear chains. The model predicts that the size of the ring polymer remains unchanged up to the overlap concentration c(r)(*). Beyond c(r)(*) the size of the ring shrinks according to R-r similar to c(r)(beta), where beta = 2v - 1 = -1/5 for v = 0.4. The overlap concentration depends on the degree of polymerization of the ring according to c(r)(*) similar to 1/root N-r. These predictions were tested by performing Monte Carlo simulations of ring-linear blends using the bond-fluctuation model. The results of the simulation for N-r = 150 and 300 blended at different concentrations with linear chains of the same degree of polymerization validate the scaling model.