Question

a recipe for trail mix calls for 3/4 cup of almonds for every 1/8 cup of raisins. how many cups of raisins are needed to make the trail mix with 1 cup of almonds? you’re trying to find the number of cups of raisins you would need for 1 cup of almonds. what do you need to divide 3/4 cups of almonds by to find 1 cup of almonds? almonds (cups) raisins (cups) 3/4 1/8 1?

Explanation:

Step1: Set up the proportion

Let $x$ be the number of cups of raisins for 1 cup of almonds. The ratio of almonds to raisins is $\frac{3}{4}:\frac{1}{8}$. We can set up the proportion $\frac{\frac{3}{4}}{\frac{1}{8}}=\frac{1}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $\frac{3}{4}x=\frac{1}{8}\times1$.

Step3: Solve for $x$

We have $x = \frac{1}{8}\div\frac{3}{4}=\frac{1}{8}\times\frac{4}{3}=\frac{1\times4}{8\times3}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$