Questions: If x varies directly as y, and x=9 when y=3, find x when y=6. x=

Solution Steps

To solve this problem, we need to use the concept of direct variation. If \( x \) varies directly as \( y \), then \( x = ky \) for some constant \( k \). First, we find \( k \) using the given values of \( x \) and \( y \). Then, we use this constant to find the new value of \( x \) when \( y = 6 \).

Since \( x \) varies directly as \( y \), we can express this relationship as: \[ x = ky \] Using the given values \( x = 9 \) when \( y = 3 \), we can find the constant \( k \): \[ k = \frac{x}{y} = \frac{9}{3} = 3.0 \]

Now that we have determined \( k = 3.0 \), we can find the value of \( x \) when \( y = 6 \): \[ x = ky = 3.0 \times 6 = 18.0 \]

Final Answer