Question

a recipe for trail mix calls for 3/4 cup of almonds for every 1/5 cup of raisins. how many cups of raisins are needed to make the trail mix with 1 cup of almonds? start by setting up a table that could be used to find the number of cups of raisins youll need if you use 1 cup of almonds to make trail mix. almonds (cups) raisins (cups)

Explanation:

Step1: Set up proportion

Let $x$ be the number of cups of raisins for 1 cup of almonds. The ratio of almonds to raisins is $\frac{3}{4}:\frac{1}{5}$. So we have the proportion $\frac{\frac{3}{4}}{\frac{1}{5}}=\frac{1}{x}$.

Step2: Cross - multiply

Cross - multiplying gives $\frac{3}{4}x=\frac{1}{5}\times1$, which simplifies to $\frac{3}{4}x = \frac{1}{5}$.

Step3: Solve for $x$

Multiply both sides by $\frac{4}{3}$ to isolate $x$. So $x=\frac{1}{5}\times\frac{4}{3}=\frac{4}{15}$.

Answer:

$\frac{4}{15}$