If xx and yy vary directly and yy is 8 when xx is 12, find yy when xx is 6.

Answer 1

To solve the problem, we start by establishing the direct variation relationship between $x$ and $y$. This means we can express the relationship as:

$$y=kx$$

where $k$ is the constant of variation.

From the problem, we know that $y=8$ when $x=12$. We can use this information to find the value of $k$:

$$8=k(12)$$

To find $k$, we divide both sides by 12:

$$k=\frac{8}{12}=\frac{2}{3}$$

Now that we have the constant $k$, we can use it to find $y$ when $x=6$:

$$y=kx=\frac{2}{3}(6)$$

Calculating this gives:

$$y=\frac{2\cdot 6}{3}=\frac{12}{3}=4$$

Therefore, when $x=6$, $y$ is $\boxed{{\displaystyle 4}}$.