Last month, Sara, Ryan, and Taylor received a total of 882 emails. If Sara received 25% more emails than the sum of the number of emails received by Ryan and Taylor, how many emails did Sara received?

Options

A. `448`
B. `486`
C. `490`
D. `504`

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information provided.

### Step 1: Define the Variables
Let:
- \( S \) = Number of emails received by Sara
- \( R \) = Number of emails received by Ryan
- \( T \) = Number of emails received by Taylor

### Step 2: Set Up the Total Emails Equation
According to the problem, the total number of emails received by Sara, Ryan, and Taylor is 882. Therefore, we can write the equation:
\[ S + R + T = 882 \quad \text{(Equation 1)} \]

### Step 3: Set Up the Relation for Sara's Emails
The problem states that Sara received 25% more emails than the sum of the emails received by Ryan and Taylor. This can be expressed as:
\[ S = 1.25(R + T) \quad \text{(Equation 2)} \]

### Step 4: Substitute \( R + T \) from Equation 1 into Equation 2
From Equation 1, we can express \( R + T \) in terms of \( S \):
\[ R + T = 882 - S \]
Now substitute this into Equation 2:
\[ S = 1.25(882 - S) \]

### Step 5: Solve for \( S \)
Distributing the 1.25:
\[ S = 1.25 \times 882 - 1.25S \]
Now, combine like terms:
\[ S + 1.25S = 1.25 \times 882 \]
\[ 2.25S = 1.25 \times 882 \]
To isolate \( S \), divide both sides by 2.25:
\[ S = \frac{1.25 \times 882}{2.25} \]

### Step 6: Calculate \( S \)
Calculating the right side:
\[ S = \frac{1102.5}{2.25} \approx 490 \]

### Conclusion
Thus, the number of emails received by Sara is:
\[ \boxed{490} \]