Question

If y varies inversely with x, and y=-5 when x=20, find x when y=-4

Answer 1

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

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

where \( k \) is a constant. Given that \( y = -5 \) when \( x = 20 \), we can find \( k \):

\[
-5 = \frac{k}{20}
\]

Multiplying both sides by 20 gives:

\[
k = -5 \times 20 = -100
\]

Now, we have the relationship:

\[
y = \frac{-100}{x}
\]

Next, we want to find \( x \) when \( y = -4 \). Substituting \( y = -4 \) into the equation gives:

\[
-4 = \frac{-100}{x}
\]

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

\[
-4x = -100
\]

Now, divide both sides by -4:

\[
x = \frac{-100}{-4} = 25
\]

Thus, when \( y = -4 \), \( x = 25 \).

The final answer is:

\[
\boxed{25}
\]