Priya is planning to send her favorite dry rub recipe to a friend who lives in France. Before sending the recipe, Priya wants to convert the American customary units in the instructions into metric units so that her friend will easily be able to understand the measurements. IF the recipe calls for a ratio of four ounces of paprika to every seven ounces of chili powder, and if priya's friend is planning to make a large batch of dry rub with 91 total ounces of chili powder, approximately how many total grams of paprika and chili powder will the recipe require? (1 ounce=28.3 grams)

Options

A. 4,047grams
B. 4,521 grams
C. 4,925 grams
D. 5,149 grams

Answer

To solve the problem step by step, we will follow the given instructions and perform the necessary calculations.

### Step 1: Understand the Ratio
The recipe calls for a ratio of 4 ounces of paprika to every 7 ounces of chili powder. This can be expressed as:
\[ \frac{p}{c} = \frac{4}{7} \]
where \( p \) is the amount of paprika and \( c \) is the amount of chili powder.

**Hint:** Remember that ratios can be expressed as fractions to relate two quantities.

### Step 2: Identify the Amount of Chili Powder
According to the problem, Priya's friend is using 91 ounces of chili powder. Therefore, we have:
\[ c = 91 \text{ ounces} \]

**Hint:** Substitute the known value into the ratio equation to find the unknown.

### Step 3: Substitute and Solve for Paprika
Now we substitute \( c = 91 \) into the ratio equation:
\[ \frac{p}{91} = \frac{4}{7} \]
To find \( p \), we can cross-multiply:
\[ p = \frac{4}{7} \times 91 \]
Calculating this gives:
\[ p = \frac{4 \times 91}{7} = \frac{364}{7} = 52 \text{ ounces} \]

**Hint:** Cross-multiplication is a useful technique for solving proportions.

### Step 4: Calculate Total Ounces
Now we need to find the total amount of paprika and chili powder combined:
\[ \text{Total ounces} = p + c = 52 + 91 = 143 \text{ ounces} \]

**Hint:** Adding the two quantities gives the total amount required.

### Step 5: Convert Ounces to Grams
To convert ounces to grams, we use the conversion factor \( 1 \text{ ounce} = 28.3 \text{ grams} \). Therefore, we calculate:
\[ \text{Total grams} = 143 \text{ ounces} \times 28.3 \text{ grams/ounce} \]
Calculating this gives:
\[ \text{Total grams} = 143 \times 28.3 \approx 4047.9 \text{ grams} \]
Rounding to the nearest whole number, we get approximately 4047 grams.

**Hint:** Multiplying by the conversion factor allows you to change units from ounces to grams.

### Conclusion
The total grams of paprika and chili powder required for the recipe is approximately:
\[ \boxed{4047 \text{ grams}} \]