To find the whole-to-part ratio for the total refreshments to boxes of orange juice, we first need to calculate the total number of refreshments.
Total refreshments = number of lemonades + number of bottles of water + number of boxes of orange juice.
Total refreshments = 13 (lemonades) + 14 (water) + 12 (orange juice) = 39.
Now, the whole-to-part ratio (total refreshments to boxes of orange juice) is given by the fraction of total refreshments to the number of boxes of orange juice.
This can be expressed as:
\[ \text{Whole-to-part ratio} = \frac{\text{Total refreshments}}{\text{Boxes of orange juice}} = \frac{39}{12}. \]
So the answer is \( \frac{39}{12} \).