10. (12 points) There are a total of 62 large and small boxes. Small boxes weigh 5 per ton, and large boxes weigh 3 per ton. Now, these boxes need to be transported using a truck. If large boxes are loaded first, after all the large boxes are loaded, the truck can still fit 15 small boxes. If small boxes are loaded first, after all the small boxes are loaded, the truck can still fit 15 large boxes. How many of these boxes are large? $\qquad$
【Solution】Solution: Let there be $x$ large boxes, then there are $62-x$ small boxes, so the weight of the large boxes is $\frac{\mathrm{x}}{3}$ tons, and the weight of the small boxes is $\frac{62-x}{5}$ tons, so $\frac{\mathrm{x}}{3}+15 \div 5 \times 1=\frac{62-\mathrm{x}}{5}+15 \div 3 \times 1$
$$
\begin{array}{c}
\frac{x}{3}+3=\frac{62-x}{5}+5 \\
\frac{x}{3}+3=-\frac{x}{5}+17.4 \\
\frac{x}{3}+3+\frac{x}{5}=-\frac{x}{5}+17.4+\frac{x}{5} \\
\frac{8}{15} x+3=17.4 \\
\frac{8}{15} x+3-3=17.4-3 \\
\frac{8}{15} x=14.4 \\
\frac{8}{15} \div \frac{8}{15}=14.4 \div \frac{8}{15} \\
x=27
\end{array}
$$

Answer: There are 27 large boxes.
Therefore, the answer is: 27.