Question

write and solve the solution for the direct variation y varies directly with x if y = 5 when x = 55. Then find the value of y when x = 22

Answer 1

In direct variation, the relationship between \( y \) and \( x \) can be expressed by the equation:

\[
y = kx
\]

where \( k \) is the constant of variation.

Given that \( y = 5 \) when \( x = 55 \), we can substitute these values into the equation to find \( k \):

\[
5 = k \cdot 55
\]

Now, solving for \( k \):

\[
k = \frac{5}{55} = \frac{1}{11}
\]

Now that we have the constant of variation \( k \), we can express the relationship as:

\[
y = \frac{1}{11}x
\]

Next, we need to find the value of \( y \) when \( x = 22 \). We substitute \( x \) into the equation:

\[
y = \frac{1}{11} \cdot 22
\]

Calculating that gives:

\[
y = \frac{22}{11} = 2
\]

Thus, the value of \( y \) when \( x = 22 \) is:

\[
\boxed{2}
\]