A recipe calls for one half
 cup of ingredient A for every 1 and one fifth
 cups of ingredient B. You use 2 cups of ingredient A. How many cups of ingredient B do you​ need?


To solve this problem, we'll use the given ratio between ingredient A and ingredient B and apply it to the amount of ingredient A you're using.

### Step 1: Understand the ratio
The ratio given is:
- \( \frac{1}{2} \) cup of ingredient A for every \( 1 \frac{1}{5} \) cups of ingredient B.

First, convert the mixed number \( 1 \frac{1}{5} \) into an improper fraction:
\[
1 \frac{1}{5} = \frac{6}{5} \text{ cups of ingredient B}
\]

So the ratio can be written as:
\[
\frac{1}{2} \text{ cup of A} : \frac{6}{5} \text{ cups of B}
\]

### Step 2: Set up the proportion
Let \( x \) be the amount of ingredient B needed for 2 cups of ingredient A. Set up the proportion based on the given ratio:
\[
\frac{1/2}{6/5} = \frac{2}{x}
\]

### Step 3: Solve the proportion
First, simplify the left side of the equation:
\[
\frac{1/2}{6/5} = \frac{1}{2} \times \frac{5}{6} = \frac{5}{12}
\]

Now the equation is:
\[
\frac{5}{12} = \frac{2}{x}
\]

Cross-multiply to solve for \( x \):
\[
5x = 12 \times 2
\]
\[
5x = 24
\]
\[
x = \frac{24}{5} = 4.8
\]

### Step 4: Conclusion
You need **4.8 cups** of ingredient B.

Would you like further details on any step? Here are five related questions you might consider:

1. How do you convert a mixed number to an improper fraction?
2. Can you explain cross-multiplication in more detail?
3. How do you determine ratios in recipes?
4. What if the recipe called for a different amount of ingredient A?
5. How would this calculation change if the ratios were reversed?

**Tip:** Always ensure that units match when setting up proportions, particularly in recipes and measurements.

A recipe calls for one half cup of ingredient A for every 1 and one fifth cups of ingredient B. You use 2 cups of ingredient A. How many cups of ingredient B do you need?

Learn how to calculate the proportion of ingredients in a recipe when given a specific ratio. This problem involves solving a proportion for ingredient B when using 2 cups of ingredient A. Key concepts include ratios, proportions, and fraction conversion. Suitable for Grades 6-8.

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