Question
X varies YZ when Y=2, Z=3, X=30. Find when y=4 and z=6
Answers
GPT-4o mini
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**.
\[
X = k \cdot Y \cdot Z
\]
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**.