We can solve this problem by applying the rule of three.
6a) We have
[tex]\begin{gathered} 1\text{ recipe ---- }\frac{3}{4}\text{pound potatoes} \\ 3\text{ recipes ----- x} \end{gathered}[/tex]where x correspond to the pound potatoes for 3 recipes.
Then, x is given by
[tex]x=\frac{3\times\frac{3}{4}}{1}[/tex]which gives
[tex]\begin{gathered} x=3\times\frac{3}{4} \\ x=\frac{9}{4} \end{gathered}[/tex]Therefore, the answer for 6a is
[tex]\frac{9}{4}\text{ pound of potatoes}[/tex]6b)
Similarly,
[tex]\begin{gathered} 1\text{ recipe ----- }\frac{1}{2}cup\text{ of beans} \\ 3\text{ recipes ---- y} \end{gathered}[/tex]where y corresponds to the cups of beams for 3 recipes. Then, y is given by
[tex]y=\frac{3\times\frac{1}{2}}{1}[/tex]which gives
[tex]\begin{gathered} y=3\times\frac{1}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Therefore, the answer for 6b is
[tex]\frac{3}{2}\text{ cups of gre}en\text{ beans}[/tex]6c)
In this case, we have
[tex]\begin{gathered} 1\text{ recipe ---- }1\frac{3}{4}\text{ tomatoes} \\ 3\text{ recipes ----- z} \end{gathered}[/tex]where z corresponds to the number of cups of tomatoes for 3 recipes. Then, z is given by
[tex]z=\frac{3\times1\frac{3}{4}}{1}[/tex]which gives
[tex]z=3\times1\frac{3}{4}[/tex]In order to obtain the product, we need to convert the mixed fraction into a simple fraction form, that is
[tex]1\frac{3}{4}=\frac{4\times1+3}{4}=\frac{7}{4}[/tex]then, we have
[tex]z=3\times\frac{7}{4}[/tex]And the answer for 6c is
[tex]z=\frac{21}{4}\text{ cups of tomatoes}[/tex]