Question

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 \( \boxed{4} \).