Let the number of William's crackers be \( W \) and the number of Daphne's crackers be \( D \). According to the problem, the ratio of William's crackers to Daphne's is given by:
\[ \frac{W}{D} = \frac{3}{5} \]
This can be rewritten as:
\[ 5W = 3D \]
We also know that the total number of crackers is 48:
\[ W + D = 48 \]
Now we have the two equations:
- \( 5W = 3D \)
- \( W + D = 48 \)
From the second equation, we can express \( W \) in terms of \( D \):
\[ W = 48 - D \]
Now, substitute this expression for \( W \) into the first equation:
\[ 5(48 - D) = 3D \]
Expanding this gives:
\[ 240 - 5D = 3D \]
Now, combine like terms:
\[ 240 = 8D \]
To find \( D \), we divide both sides by 8:
\[ D = \frac{240}{8} = 30 \]
Thus, Daphne has 30 crackers. To find out how many William has, substitute back into the equation for \( W \):
\[ W = 48 - D = 48 - 30 = 18 \]
Finally, we can verify the ratio:
\[ \frac{W}{D} = \frac{18}{30} = \frac{3}{5} \]
This confirms that the solution is consistent. Therefore, Daphne has \( \boxed{30} \) crackers.
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