In a small town, the local bakery decided to create special pastry boxes for the holidays. Each box contains a mix of pastries: $3$ cinnamon rolls, $2$ apple turnovers, and $5$ chocolate eclairs. The cost of $1$ cinnamon roll is $2$, $1$ apple turnover is $3$, and $1$ chocolate eclair is $4$. The bakery has a budget of $100$ for creating these pastry boxes.

How many pastry boxes can the bakery prepare without exceeding the budget?