To solve the problem where [tex]\(y\)[/tex] varies directly with [tex]\(x\)[/tex], we start by noting the form of the relationship: [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is a constant of proportionality.
1. Determine the constant [tex]\( k \)[/tex] using the given values:
- We know that [tex]\( y = 27 \)[/tex] when [tex]\( x = 9 \)[/tex].
- Substitute these values into the direct variation equation:
[tex]\[
y = kx \implies 27 = k \cdot 9
\][/tex]
- To find [tex]\( k \)[/tex], divide both sides by 9:
[tex]\[
k = \frac{27}{9} = 3
\][/tex]
2. Use the constant [tex]\( k \)[/tex] to find the unknown value of [tex]\( x \)[/tex] when [tex]\( y = 30 \)[/tex]:
- The equation now is [tex]\( y = 3x \)[/tex].
- Substitute [tex]\( y = 30 \)[/tex] into the equation to find [tex]\( x \)[/tex]:
[tex]\[
30 = 3x
\][/tex]
- To solve for [tex]\( x \)[/tex], divide both sides by 3:
[tex]\[
x = \frac{30}{3} = 10
\][/tex]
Therefore, when [tex]\( y = 30 \)[/tex], [tex]\( x \)[/tex] is [tex]\( 10 \)[/tex].
