[tex]y[/tex] varies directly with [tex]x[/tex]. [tex]y[/tex] is 32 when [tex]x[/tex] is 8. What is [tex]x[/tex] when [tex]y[/tex] is 12?

[tex]x = [?][/tex]



Answer :

Given that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we can express this relationship with the equation:

[tex]\[ y = kx \][/tex]

where [tex]\( k \)[/tex] is a constant of proportionality.

To find [tex]\( k \)[/tex], we use the given values: [tex]\( y = 32 \)[/tex] when [tex]\( x = 8 \)[/tex].

Substitute these values into the equation:

[tex]\[ 32 = k \cdot 8 \][/tex]

Solving for [tex]\( k \)[/tex], we get:

[tex]\[ k = \frac{32}{8} = 4 \][/tex]

Now, we have the proportionality constant [tex]\( k = 4 \)[/tex].

Next, we need to find the value of [tex]\( x \)[/tex] when [tex]\( y \)[/tex] is 12.

Using the direct variation equation [tex]\( y = kx \)[/tex] and substituting [tex]\( y = 12 \)[/tex] and [tex]\( k = 4 \)[/tex]:

[tex]\[ 12 = 4x \][/tex]

Solving for [tex]\( x \)[/tex], we divide both sides of the equation by 4:

[tex]\[ x = \frac{12}{4} = 3 \][/tex]

Therefore, when [tex]\( y \)[/tex] is 12, [tex]\( x \)[/tex] is:

[tex]\[ x = 3 \][/tex]