Questions: If y varies jointly as x and z, find y when x=6 and z=5 if the constant of variation is k=3. y=

Solution Steps

To solve this problem, we use the concept of joint variation, which states that if \( y \) varies jointly as \( x \) and \( z \), then \( y = kxz \), where \( k \) is the constant of variation. Given \( k = 3 \), \( x = 6 \), and \( z = 5 \), we substitute these values into the equation to find \( y \).

Given that \( y \) varies jointly as \( x \) and \( z \), we can express this relationship mathematically as: \[ y = kxz \] where \( k \) is the constant of variation.

We are provided with the values \( k = 3 \), \( x = 6 \), and \( z = 5 \). Substituting these values into the equation gives: \[ y = 3 \cdot 6 \cdot 5 \]

Now, we perform the multiplication: \[ y = 3 \cdot 6 = 18 \] \[ y = 18 \cdot 5 = 90 \]

Final Answer