Shirley went to the store planning to buy $120$ balloons for $10$ dollars. When she arrived, she was surprised to nd that the balloons were on sale for $20$ percent less than expected. How many balloons could Shirley buy for her $10$ dollars?
1. Initially, Shirley planned to buy 120 balloons for $10. This implies that the expected price per balloon is:
   \[
   \text{Expected price per balloon} = \frac{10 \text{ dollars}}{120 \text{ balloons}} = \frac{1}{12} \text{ dollars per balloon}
   \]

2. The balloons were on sale for 20% less than expected. Therefore, the sale price per balloon is:
   \[
   \text{Sale price per balloon} = \left(1 - 0.20\right) \times \frac{1}{12} \text{ dollars per balloon} = 0.80 \times \frac{1}{12} \text{ dollars per balloon} = \frac{0.80}{12} \text{ dollars per balloon} = \frac{2}{30} \text{ dollars per balloon} = \frac{1}{15} \text{ dollars per balloon}
   \]

3. With $10, the number of balloons Shirley can buy at the sale price is:
   \[
   \text{Number of balloons} = \frac{10 \text{ dollars}}{\frac{1}{15} \text{ dollars per balloon}} = 10 \times 15 = 150 \text{ balloons}
   \]

Therefore, Shirley can buy 150 balloons for her $10.

The final answer is $\boxed{150}$.