210 is p% greater than 30. What is the value of p?

To find the value of $p$ where 210 is $p\%$ greater than 30, we can follow these steps:

1. Break Down the Problem

   We need to determine the percentage increase from 30 to 210. This involves finding the difference between 210 and 30, and then expressing this difference as a percentage of 30.

2. Relevant Concepts

   The formula to calculate the percentage increase is: $\text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$

3. Analysis and Detail

   1. Calculate the difference between the new value and the original value: $210 - 30 = 180$
   2. Use the formula to find the percentage increase: $\text{Percentage Increase} = \left( \frac{180}{30} \right) \times 100$
   3. Simplify the expression: $\frac{180}{30} = 6$ $6 \times 100 = 600$

4. Verify and Summarize

   Verify the calculations:

   • The difference is correctly calculated as 180.
   • Dividing 180 by 30 gives 6.
   • Multiplying by 100 gives a percentage increase of 600%.

Final Answer

The value of $p$ is 600.