Respuesta :
we can make a relation
makayla uses 2 1/2 pounds of chocolate to make exactly 3 1/3 dozen truffles
[tex]\begin{gathered} 2\frac{1}{2}\longrightarrow3\frac{1}{3} \\ \\ \end{gathered}[/tex]How many pounds of chocolate would she need to make 5 dozen truffles?
[tex]x\longrightarrow5[/tex]where x is the pounds of chocolate to make 5 dozen truffles
Solving
we group the raltions
[tex]\begin{gathered} 2\frac{1}{2}\longrightarrow3\frac{1}{3} \\ \\ x\longrightarrow5 \end{gathered}[/tex]we transform mixed numbers to be easier
[tex]\begin{gathered} 2\frac{1}{2}\longrightarrow\frac{(2\times2)+1}{2}=\frac{5}{2} \\ \\ 3\frac{1}{3}\longrightarrow\frac{(3\times3)+1}{3}=\frac{10}{3} \end{gathered}[/tex][tex]\begin{gathered} \frac{5}{2}\longrightarrow\frac{10}{3} \\ \\ x\longrightarrow5 \end{gathered}[/tex]we can use cross multiplication to solve:
multiply diagonal numbers (5 and 5/2) and divide by 10/3 to find x
[tex]\begin{gathered} x=\frac{(5\times\frac{5}{2})}{\frac{10}{3}} \\ \\ x=\frac{\frac{25}{2}}{\frac{10}{3}} \\ \\ x=\frac{25\times3}{10\times2} \\ \\ x=\frac{75}{20}=\frac{15}{4} \end{gathered}[/tex]now transform to mixed numbers
[tex]\begin{gathered} \frac{12}{4}+\frac{3}{4} \\ \\ 3+\frac{3}{4}=3\frac{3}{4} \end{gathered}[/tex]then Makayla uses 3 3/4 chocolate pounds to make 5 dozen
