3. (10 points) A store bought a batch of greeting cards at 21 cents each, and sold them for a total of 14.57 yuan. If each card was sold at the same price, and the selling price did not exceed twice the purchase price, then the store made a profit of $\qquad$yuan.

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【Analysis】14.57 yuan $=1457$ fen, 2 jiao 1 fen $=21$ fen, according to "total price $=$ unit price $\times$ quantity" we know: 1457 is the product of the number of items and the price per item, so first decompose 1457 into the product of two factors, then solve based on if the price per item is the same, and does not exceed twice the purchase price (i.e., $21 \times 2=42$ fen).

【Solution】Solution: 14.57 yuan $=1457$ fen,
$$
1457=31 \times 47
$$
2 jiao 1 fen $=21$ fen
$$
21 \times 2=42 \text { (fen) }
$$

Since the price per item does not exceed twice the purchase price,
47 is the quantity, 31 fen is the selling price;
The store's profit: $(31-21) \times 47$
$$
\begin{array}{l}
=10 \times 47 \\
=470 \text { (fen) } \\
=4.7 \text { yuan; }
\end{array}
$$

Answer: The store made a profit of 4.7 yuan.
The answer is: 4.7.