Questions: y varies jointly as x and z. y=36 when x=6 and z=2. Find y when x=7 and z=5.

Solution Steps

To solve this problem, we need to use the concept of joint variation. Since \( y \) varies jointly as \( x \) and \( z \), we can express this relationship as \( y = kxz \), where \( k \) is the constant of variation. First, we will find the value of \( k \) using the given values \( y = 36 \), \( x = 6 \), and \( z = 2 \). Then, we will use this value of \( k \) to find \( y \) when \( x = 7 \) and \( z = 5 \).

Given that \( y \) varies jointly as \( x \) and \( z \), we can express this relationship as: \[ y = kxz \] Using the values \( y = 36 \), \( x = 6 \), and \( z = 2 \), we can solve for \( k \): \[ k = \frac{y}{xz} = \frac{36}{6 \cdot 2} = \frac{36}{12} = 3.0 \]

Now, we need to find \( y \) when \( x = 7 \) and \( z = 5 \). Using the previously calculated value of \( k \): \[ y = kxz = 3.0 \cdot 7 \cdot 5 \] Calculating this gives: \[ y = 3.0 \cdot 35 = 105.0 \]

Final Answer