Respuesta :
GIVEN:
We are given a recipe which requires four and half cups of milk to one cup of flour.
Required:
If two and one-quarter cups of milk is used, what quantity of flour will be needed accoeding to the recipe.
Step-by-step solution;
For the recipe provided we have the following ratio;
[tex]\begin{gathered} RATIO \\ \\ Milk:flour=4\frac{1}{2}:1 \end{gathered}[/tex]If two and one-quater cups of milk is used, and we do not know the amount of flour used, we can represent flour by f in this ratio and that would now be;
[tex]Milk:Flour=2\frac{1}{4}:f[/tex]Since the ratios are the same for the recipe even with different quantities of milk and flour, then both ratios can be equated and we'll have the following equation;
[tex]\begin{gathered} 4\frac{1}{2}:1=2\frac{1}{4}:f \\ \\ \frac{9}{2}:1=\frac{9}{4}:f \end{gathered}[/tex]Therefore, we can now set up the following equation;
[tex]\begin{gathered} \frac{9}{2}\div1=\frac{9}{4}\div f \\ \\ \frac{9}{2}=\frac{9}{4}\times\frac{1}{f} \\ \\ \frac{9}{2}=\frac{9}{4f} \end{gathered}[/tex]Now we cross multiply and we have;
[tex]\begin{gathered} f=\frac{9\times2}{4\times9} \\ \\ f=\frac{18}{36} \\ \\ f=\frac{1}{2} \end{gathered}[/tex]Therefore, for 2 and 1/4 cups of milk then 1/2 cup of flour will be used.
ANSWER:
[tex]flour=\frac{1}{2}\text{ }cup[/tex]