Mark has $$100,000$ to invest. His financial consultant advises him to diversify his investment in three types of bonds: short$-$term, intermediate$-$term, and long$-$term. The short$-$term bonds pay $3\%,$ the intermediate$-$term bonds pay $4\%,$ and the long$-$term bonds pay $6\%$ simple interest per year. Mark wishes to realize a total annual income of $4\mathrm{.}5\%,$ with equal amounts invested in short$-$ and intermediate$-$term bonds. How much should he invest in each type of bond?