To find the payout check if it was just Alexis and her two favorite co-workers, we can use the concept of inverse variation. When the payout is stated to vary inversely with the number of winners, we can describe this relationship mathematically.
Let \( P \) represent the payout, and \( n \) represent the number of winners. The relationship can be expressed as:
\[ P = k \cdot \frac{1}{n} \]
where \( k \) is a constant.
- Determine the constant \( k \) using the initial situation: In the given situation, there are 8 winners (Alexis and her 7 co-workers), and each received a payout of $4.65 million. Therefore, we can write:
\[ P = 4.65 \text{ million} \] \[ n = 8 \]
Substituting these values into the equation gives:
\[ 4.65 = k \cdot \frac{1}{8} \]
To find \( k \):
\[ k = 4.65 \cdot 8 = 37.2 \text{ million} \]
- Find the payout for just Alexis and her two favorite co-workers: In this case, there would be 3 winners (Alexis and her two favorite co-workers). We can now use the value of \( k \) to find the new payout:
\[ n = 3 \]
Using the formula for \( P \):
\[ P = \frac{k}{n} = \frac{37.2}{3} \]
Calculating this gives:
\[ P = 12.4 \text{ million} \]
Thus, if it was just Alexis and her two favorite co-workers, the payout check would have been $12.4 million.
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