Question

If y varies inversely with x, and y=8 When x=10, find x when y=4

Answer 1

If \( y \) varies inversely with \( x \), this relationship can be expressed as:

\[
y = \frac{k}{x}
\]

where \( k \) is a constant.

Given that \( y = 8 \) when \( x = 10 \), we can first find the value of \( k \):

\[
8 = \frac{k}{10}
\]

To find \( k \), multiply both sides by 10:

\[
k = 8 \times 10 = 80
\]

Now that we have the constant \( k \), the relationship can be expressed as:

\[
y = \frac{80}{x}
\]

Now, we need to find \( x \) when \( y = 4 \):

\[
4 = \frac{80}{x}
\]

To solve for \( x \), multiply both sides by \( x \):

\[
4x = 80
\]

Now, divide both sides by 4:

\[
x = \frac{80}{4} = 20
\]

Therefore, when \( y = 4 \), \( x \) is \( 20 \).