To find the value of \( m \) when \( p = 7 \) in an inverse variation problem where \( m \) varies inversely as \( p \), we can follow these steps:
1. Write the inverse variation formula: \( y = k \), where \( k \) is a constant. In this case, \( m \) and \( p \) are inversely related, so we have \( m = k/p \).
2. Use the given values to find the constant \( k \). We are given that \( m = 30 \) when \( p = 5 \). Substitute these values into the formula: \( 30 = k/5 \). Solve for \( k \) by multiplying both sides by 5: \( k = 30 * 5 = 150 \).
3. Now that we have found the constant \( k \), we can use it to find \( m \) when \( p = 7 \). Substitute \( k = 150 \) and \( p = 7 \) into the formula: \( m = 150/7 \). Calculate this to find the value of \( m \) when \( p = 7 \).
4. Simplify the expression: \( m = 150/7 \approx 21.43 \).
Therefore, when \( p = 7 \), \( m \) is approximately 21.43 in this inverse variation problem.
