Question

A recipe for trail mix calls for
3
2
​
cup of almonds for every
5
1
​
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 you’ll need if you use 1 cup of almonds to make trail mix.
Almonds (cups) Raisins (cups)

Answer 1

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.