To find out how many cups of trail mix Orly can make with 12 cups of raisins, we can set up a proportion based on the ratio given.
Orly uses 2 cups of raisins for every 9 cups of trail mix, which gives us the ratio: \[ \text{Raisins} : \text{Trail Mix} = 2 : 9 \]
We can express this as a fraction: \[ \frac{\text{Raisins}}{\text{Trail Mix}} = \frac{2}{9} \]
Let \( x \) represent the total cups of trail mix Orly will make with 12 cups of raisins. We can set up the equation: \[ \frac{12}{x} = \frac{2}{9} \]
Now we can cross-multiply to solve for \( x \): \[ 12 \cdot 9 = 2 \cdot x \] \[ 108 = 2x \]
Next, divide both sides by 2: \[ x = \frac{108}{2} = 54 \]
Therefore, if Orly uses 12 cups of raisins, she will make 54 cups of trail mix.
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