A recipe for trail mix calls for

To find the number of cups of raisins needed for 1 cup of almonds based on the given ratio of almonds to raisins, we begin by determining the equivalent ratio from the ingredients provided. The recipe states:

• 3.2 cups of almonds for every 5.1 cups of raisins.

Let's represent the units in a table:

| Almonds (cups) | Raisins (cups) | |----------------|-----------------| | 3.2 | 5.1 | | 1 | ? |

Now, we need to find the number of cups of raisins needed for 1 cup of almonds. To do this, we can set up a proportion based on the original ratio:

\[ \frac{3.2 \text{ cups of almonds}}{5.1 \text{ cups of raisins}} = \frac{1 \text{ cup of almonds}}{x \text{ cups of raisins}} \]

Where \(x\) represents the unknown quantity of raisins we need.

To solve for \(x\), we can cross-multiply:

\[ 3.2 \cdot x = 5.1 \cdot 1 \]

Simplifying this gives us:

\[ 3.2x = 5.1 \]

Now, divide both sides by 3.2 to isolate \(x\):

\[ x = \frac{5.1}{3.2} \]

Calculating this:

\[ x \approx 1.59375 \]

So, to make the trail mix with 1 cup of almonds, you would need approximately 1.59 cups of raisins.

Now, you could complete the table with this value:

| Almonds (cups) | Raisins (cups) | |----------------|-----------------| | 3.2 | 5.1 | | 1 | 1.59375 |

This table shows the relationship between the number of cups of almonds and the corresponding cups of raisins needed for the trail mix.