Question

If \( x \) is inversely proportional to \( y \) and \( x = 8 \) when \( y = 2 \), what is \( x \) when \( y = 4 \)?

Hint:

When variables are inversely proportional, their product remains constant. You can use this property to solve for unknown values by setting up an equation and solving for the unknown.

Answer 1

Since \( x \) is inversely proportional to \( y \), we know the relationship can be expressed as: \[ x \times y = k, \] where \( k \) is a constant. 1.{Given values}: We are given that \( x = 8 \) and \( y = 2 \). Using these values, we can find the constant \( k \). Substitute the known values into the equation: \[ 8 \times 2 = 16
\Rightarrow
k = 16. \] Thus, the constant \( k \) is 16. 2.{Find \( x \) for a new value of \( y \)}: Now, we are asked to find the value of \( x \) when \( y = 4 \). Using the equation \( x \times y = k \), we substitute \( y = 4 \) and \( k = 16 \) into the equation: \[ x \times 4 = 16
\Rightarrow
x = \frac{16}{4} = 4. \] Thus, the value of \( x \) when \( y = 4 \) is \( \boxed{4} \).