Diana is baking bread, and the original recipe calls for `1 1/2` teaspoons of yeast and `2 1/2` cups of flour. Diana will use the entire contents of a packet that contains `2 1/4` teaspoons of yeast and will use the same ratio of ingredients called for in the orginal recipe. How many cups of flour will Diana use?

Options

A. `1 7/8`
B. `3 1/4`
C. `3 1/2`
D. `3 3/4`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the original recipe
The original recipe calls for:
- Yeast: \(1 \frac{1}{2}\) teaspoons
- Flour: \(2 \frac{1}{2}\) cups

### Step 2: Convert mixed numbers to improper fractions
Convert the mixed numbers to improper fractions for easier calculations:
- Yeast:
\[ 1 \frac{1}{2} = \frac{3}{2} \]
- Flour:
\[ 2 \frac{1}{2} = \frac{5}{2} \]

### Step 3: Determine the ratio of yeast to flour
The ratio of yeast to flour can be written as:
\[ \text{Ratio} = \frac{3/2}{5/2} = \frac{3}{5} \]
Thus, the ratio of yeast to flour is \(3:5\).

### Step 4: Determine the amount of yeast Diana will use
Diana will use the entire contents of a packet containing:
\[ 2 \frac{1}{4} \text{ teaspoons of yeast} \]
Convert this to an improper fraction:
\[ 2 \frac{1}{4} = \frac{9}{4} \]

### Step 5: Set up the equation using the ratio
Let \(X\) be the number of cups of flour Diana will use. According to the ratio of yeast to flour:
\[ \frac{9/4}{X} = \frac{3}{5} \]

### Step 6: Cross-multiply to solve for \(X\)
Cross-multiplying gives us:
\[ 9 \cdot 5 = 3 \cdot 4X \]
This simplifies to:
\[ 45 = 12X \]

### Step 7: Solve for \(X\)
Now, divide both sides by 12:
\[ X = \frac{45}{12} \]
Simplifying this fraction:
\[ X = \frac{15}{4} \]

### Step 8: Convert \(X\) back to a mixed number
Convert \(\frac{15}{4}\) to a mixed number:
\[ \frac{15}{4} = 3 \frac{3}{4} \]

### Conclusion
Thus, Diana will use \(3 \frac{3}{4}\) cups of flour.