X varies YZ when Y=2, Z=3, X=30. Find when y=4 and z=6

1 answer

To solve the problem, we first interpret "X varies YZ" as meaning that \( X \) is proportional to the product of \( Y \) and \( Z \). This can be expressed mathematically as:

\[ X = k \cdot Y \cdot Z \]

where \( k \) is a constant.

From the problem, we have the values when \( Y = 2 \), \( Z = 3 \), and \( X = 30 \):

\[ 30 = k \cdot 2 \cdot 3 \]

Calculating the right side:

\[ 30 = k \cdot 6 \]

Now, we can solve for \( k \):

\[ k = \frac{30}{6} = 5 \]

Next, we need to find \( X \) when \( Y = 4 \) and \( Z = 6 \):

\[ X = k \cdot Y \cdot Z = 5 \cdot 4 \cdot 6 \]

Calculating the right side:

\[ X = 5 \cdot 24 = 120 \]

Thus, when \( Y = 4 \) and \( Z = 6 \), \( X \) equals 120.