Questions: Solve the problem of joint variation using a constant of variation. Z varies jointly as W and Y. If Z=300 when W=10 and Y=15, find Z when W=50 and Y=5. The quantity indicated is Z=

Solution Steps

To solve the problem of joint variation, we first need to establish the relationship between the variables. Since \( Z \) varies jointly as \( W \) and \( Y \), we can express this as \( Z = k \cdot W \cdot Y \), where \( k \) is the constant of variation. We will first use the given values of \( Z = 300 \), \( W = 10 \), and \( Y = 15 \) to find \( k \). Once \( k \) is determined, we will use it to find the new value of \( Z \) when \( W = 50 \) and \( Y = 5 \).

Given that \( Z \) varies jointly as \( W \) and \( Y \), we can express this relationship mathematically as: \[ Z = k \cdot W \cdot Y \] where \( k \) is the constant of variation.

Using the provided values \( Z = 300 \), \( W = 10 \), and \( Y = 15 \), we can substitute these into the equation to find \( k \): \[ 300 = k \cdot 10 \cdot 15 \] This simplifies to: \[ k = \frac{300}{10 \cdot 15} = \frac{300}{150} = 2.0 \]

Now, we need to find \( Z \) when \( W = 50 \) and \( Y = 5 \). We substitute \( k \), \( W \), and \( Y \) into the joint variation equation: \[ Z = 2.0 \cdot 50 \cdot 5 \] Calculating this gives: \[ Z = 2.0 \cdot 250 = 500.0 \]

Final Answer