If \( h \) varies inversely as \( k \), and \( h=9 \) when \( k=20 \), what is the value of \( k+4 \) when \( h=15 \) ? (grid-in)

Since \( h \) varies inversely as \( k \), we can express this relationship as: \[ h = \frac{c}{k} \] where \( c \) is a constant. Given that \( h = 9 \) when \( k = 20 \), we can find the value of \( c \): \[ 9 = \frac{c}{20} \] Multiplying both sides by 20 gives: \[ c = 9 \times 20 = 180 \] Now we have the relationship: \[ h = \frac{180}{k} \] Next, we need to find the value of \( k \) when \( h = 15 \): \[ 15 = \frac{180}{k} \] To solve for \( k \), we can rearrange the equation: \[ k = \frac{180}{15} \] Calculating the right side: \[ k = 12 \] Now, we need to find \( k + 4 \): \[ k + 4 = 12 + 4 = 16 \] Thus, the value of \( k + 4 \) when \( h = 15 \) is: \[ \boxed{16} \]