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 crackers is given as:
\[ \frac{W}{D} = \frac{3}{5} \]
This implies that: \[ 5W = 3D \]
We are also informed that the total number of crackers is 48, which can be formulated as: \[ W + D = 48 \]
Now, we can express \( W \) in terms of \( D \) using the ratio:
\[ W = \frac{3}{5}D \]
Substituting this expression for \( W \) into the total number of crackers equation gives:
\[ \frac{3}{5}D + D = 48 \]
To combine the terms on the left side, convert \( D \) into a fraction with a denominator of 5:
\[ \frac{3}{5}D + \frac{5}{5}D = 48 \]
This simplifies to:
\[ \frac{8}{5}D = 48 \]
Next, we solve for \( D \) by multiplying both sides by 5:
\[ 8D = 240 \]
Now, divide both sides by 8:
\[ D = 30 \]
Thus, Daphne has \( \boxed{30} \) crackers.
To confirm this result, we can find how many crackers William has:
Using the total number of crackers:
\[ W = 48 - D = 48 - 30 = 18 \]
Now, we verify the ratio of their crackers:
\[ \frac{W}{D} = \frac{18}{30} = \frac{3}{5} \]
Since this matches the original ratio, our answer that Daphne has \( \boxed{30} \) crackers is indeed correct.
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