Question

makayla uses 2 1/2 pounds of chocolate to make exactly 3 1/3 dozen truffles. How many pounds of chocolate would she need to make 5 dozen truffles?

Answer 1

we can make a relation

makayla uses 2 1/2 pounds of chocolate to make exactly 3 1/3 dozen truffles

`\begin{gathered} 2(1)/(2)\longrightarrow3(1)/(3) \\ \\ \end{gathered}`

How many pounds of chocolate would she need to make 5 dozen truffles?​

`x\longrightarrow5`

where x is the pounds of chocolate to make 5 dozen truffles

Solving

we group the raltions

`\begin{gathered} 2(1)/(2)\longrightarrow3(1)/(3) \\ \\ x\longrightarrow5 \end{gathered}`

we transform mixed numbers to be easier

`\begin{gathered} 2(1)/(2)\longrightarrow((2*2)+1)/(2)=(5)/(2) \\ \\ 3(1)/(3)\longrightarrow((3*3)+1)/(3)=(10)/(3) \end{gathered}`
`\begin{gathered} (5)/(2)\longrightarrow(10)/(3) \\ \\ x\longrightarrow5 \end{gathered}`

we can use cross multiplication to solve:

multiply diagonal numbers (5 and 5/2) and divide by 10/3 to find x

`\begin{gathered} x=((5*(5)/(2)))/((10)/(3)) \\ \\ x=((25)/(2))/((10)/(3)) \\ \\ x=(25*3)/(10*2) \\ \\ x=(75)/(20)=(15)/(4) \end{gathered}`

now transform to mixed numbers

`\begin{gathered} (12)/(4)+(3)/(4) \\ \\ 3+(3)/(4)=3(3)/(4) \end{gathered}`

then Makayla uses 3 3/4 chocolate pounds to make 5 dozen