To find the ratio of the number of sundaes without nuts to the total number of sundaes, we first need to calculate the total number of sundaes sold.
Scarlett's Ice Creamery sold:
- 33 sundaes with nuts
- 39 sundaes without nuts
Now, let's calculate the total number of sundaes:
\[ \text{Total sundaes} = \text{Sundaes with nuts} + \text{Sundaes without nuts} = 33 + 39 = 72 \]
Next, we find the ratio of the number of sundaes without nuts to the total number of sundaes:
\[ \text{Ratio} = \frac{\text{Sundaes without nuts}}{\text{Total sundaes}} = \frac{39}{72} \]
To simplify this fraction, we can find the greatest common divisor (GCD) of 39 and 72. The GCD is 3 (since 39 = 3 × 13 and 72 = 3 × 24).
Now we simplify the fraction:
\[ \frac{39 \div 3}{72 \div 3} = \frac{13}{24} \]
Therefore, the ratio of the number of sundaes without nuts to the total number of sundaes is:
\[ \frac{13}{24} \]