To find out how many cups of trail mix Orly can make with 12 cups of raisins, we can start by establishing the ratio based on the information provided:
Orly uses 2 cups of raisins to make 8 cups of trail mix.
We can set up a proportion to find out how many cups of trail mix can be made with 12 cups of raisins:
\[ \text{If } 2 \text{ cups of raisins} \rightarrow 8 \text{ cups of trail mix,} \] \[ \text{Then } 12 \text{ cups of raisins} \rightarrow x \text{ cups of trail mix.} \]
We can set up the equation like this:
\[ \frac{2 \text{ cups of raisins}}{8 \text{ cups of trail mix}} = \frac{12 \text{ cups of raisins}}{x \text{ cups of trail mix}} \]
To solve for \(x\), cross-multiply:
\[ 2x = 12 \times 8 \] \[ 2x = 96 \]
Now, divide both sides by 2:
\[ x = \frac{96}{2} = 48 \]
Therefore, if Orly uses 12 cups of raisins, she will make 48 cups of trail mix.
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