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)
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)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
- **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.
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