Certainly! Let's walk through the solution step-by-step.
We need to find out how many cups of flour are required if we adjust a recipe that originally calls for 5 cups of peanuts and 4 cups of flour to use only 2 cups of peanuts.
Here's our table to start with:
[tex]\[
\begin{tabular}{|c|c|}
\hline
Cups of Peanuts & Cups of Flour \\
\hline
5 & 4 \\
\hline
2 & ? \\
\hline
\end{tabular}
\][/tex]
Notice that this problem involves a proportional relationship between the amount of peanuts and flour. Therefore, we can set up a proportion based on the given information. Let's denote the unknown quantity (the cups of flour needed for 2 cups of peanuts) by [tex]\( x \)[/tex].
The proportion can be set up as follows:
[tex]\[
\frac{\text{Cups of Peanuts}}{\text{Cups of Flour}} = \frac{5}{4} = \frac{2}{x}
\][/tex]
To solve for [tex]\( x \)[/tex], we'll use cross-multiplication:
[tex]\[
5x = 4 \cdot 2
\][/tex]
Now, simplify the right-hand side:
[tex]\[
5x = 8
\][/tex]
Next, solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[
x = \frac{8}{5} = 1.6
\][/tex]
Therefore, you will need 1.6 cups of flour to use for 2 cups of peanuts.
In conclusion, if you adjust the recipe to use 2 cups of peanuts, you'll need 1.6 cups of flour.
