To find the total cost of the large box containing 25 bottles of drinks, you can multiply the number of bottles by the price per bottle.
The cost for one bottle is $1.75. Therefore, to find the total cost for 25 bottles:
\[ \text{Total Cost} = \text{Number of Bottles} \times \text{Price per Bottle} \]
\[ \text{Total Cost} = 25 \times 1.75 \]
Calculating this gives:
\[ 25 \times 1.75 = 43.75 \]
Thus, the cost of the large box is:
\[ x = 43.75 \]
So the final answer, rounded to the nearest hundredth, is:
\[ \boxed{43.75} \]