饮丹

我们将第一个玻璃的体积表示为 $\textit{x}$，将第二个玻璃的体积表示为 $\textit{y}$。我们现在可以将这两个卷等同为 $\frac{3}{4}x = \frac{2}{3}y$。这是因为第一个玻璃杯 (x) 已满 $\frac{3}{4}$，将其全部内容物倒入第二个玻璃杯 (y) 后，它已满 $\frac{2}{3}$。所以第一个杯子的 $\frac{3}{4}$ 等于第二个杯子的 $\frac{2}{3}$。现在要求我们求解第一个玻璃的体积除以第二个玻璃的体积的分数或比率。我们被要求求解 $\frac{x}{y}$ 的比率。我们可以对原始等式进行代数运算以获得 $\frac{x}{y} = \frac{\frac{2}{3}}{\frac{3}{4}}$。或者，$\frac{x}{y} = \frac{8}{9}$。因此体积比为 $\frac{8}{9}$（第二个比第一个大 $\frac{1}{8}$ 或 $12.5$）。

---

Original Explanation

Let’s denote the volume of the first glass as $\textit{x}$, and the volume of the second glass as $\textit{y}$. We can now equate the two volumes as $\frac{3}{4}x = \frac{2}{3}y$. This is because the first glass (x) was $\frac{3}{4}$ full, and after pouring it’s entire contents into the second glass (y), it became $\frac{2}{3}$ full. So $\frac{3}{4}$ of the first cup is equal to $\frac{2}{3}$ of the second glass. We are now asked to solve for the fraction or ratio of the volume of the first glass divided by the volume of the second. We’re asked to solve for the ratio $\frac{x}{y}$. We can perform algebraic manipulations on our original equality to attain $\frac{x}{y} = \frac{\frac{2}{3}}{\frac{3}{4}}$. Or, $\frac{x}{y} = \frac{8}{9}$. So the ratio of volumes is $\frac{8}{9}$ (the second one is larger than the first by $\frac{1}{8}$ or $12.5$).