To determine the number of weeks it will take for Miley to save enough money for the boots, we can set up the equation based on her savings.
Miley saves $25 each week. If we let \( w \) be the number of weeks, then the total amount she saves after \( w \) weeks is given by:
\[ \text{Total Savings} = 25w \]
We want her savings to equal the cost of the boots, which is $150:
\[ 25w = 150 \]
Now, we can solve for \( w \):
\[ w = \frac{150}{25} = 6 \]
Therefore, it will take Miley 6 weeks to save enough money to buy the boots.