To find the number of roast beef servings that Rick can make, we proceed as follows:
Step 1: Divide the total weight of the roast beef by the amount of weight of meat per serving, as follows:
[tex]\begin{gathered} \text{Total weight of roast beef =}2\frac{3}{4}\text{ pounds=}\frac{11}{4}\text{ pounds} \\ \text{amount of weight of meat per serving = }\frac{1}{2}\text{ pounds} \\ \text{Therefore:} \\ \text{Number }of\text{ servings =}\frac{T\text{otal weight of roast beef}}{A\text{mount of weight of meat per serving}} \\ \Rightarrow\text{ Number }of\text{ servings =}\frac{\frac{11}{4}}{\frac{1}{2}} \\ \Rightarrow\text{Number }of\text{ servings =}\frac{11}{4}\times\frac{2}{1}=\frac{22}{4}=\frac{11}{2}=5.5\text{ } \end{gathered}[/tex]Therefore, the number of roast beef servings that Rick can make is 5.5