已知 y 与 x 的平方根成反比。
求当 y 的值减少 50% 时，x 的百分比变化。 答案 ...

1. Write the inverse proportional relationship and relate the new value of $y$ to the original value.

Since $y$ is inversely proportional to $\sqrt{x}$,
$y=\frac{k}{\sqrt{x}}.$
If $y$ decreases by $50\%$, the new value is
$y_{\text{new}}=50\%\text{ of }y=\frac{1}{2}y.$

2. Find the corresponding change in $x$ and express it as a percentage change.

Let the original value be $y=\dfrac{k}{\sqrt{x}}$.

For the new value,
$\frac{1}{2}y=\frac{k}{\sqrt{x_{\text{new}}}}.$
Substitute $y=\dfrac{k}{\sqrt{x}}$:
$\frac{1}{2}\cdot \frac{k}{\sqrt{x}}=\frac{k}{\sqrt{x_{\text{new}}}}.$
Cancel $k$:
$\frac{1}{2\sqrt{x}}=\frac{1}{\sqrt{x_{\text{new}}}}.$
Hence
$\sqrt{x_{\text{new}}}=2\sqrt{x}.$
Squaring both sides,
$x_{\text{new}}=4x.$
So $x$ changes from $x$ to $4x$, an increase of $3x$.

Percentage increase
$=\frac{3x}{x}\times 100\%=300\%.$