Solve the following word problem.
Two empty storage reservoirs, X and Y, are filled with water. If an identical volume of water is pumped into both reservoirs, reservoir X becomes $\frac{3}{\mathrm{8 }}$ full and reservoir Y becomes $\frac{2}{5}$ full. The total capacity of reservoir Y is what percent of the total capacity of reservoir X?

The correct option is 93.75%.

Step-by-Step Explanation:

Let $V$ be the identical volume of water pumped into both reservoirs, X and Y.

Let $C_X$ represent the total capacity of reservoir X, and $C_Y$ represent the total capacity of reservoir Y.

Step 1: Express the total capacity of reservoir X in terms of $V$.
We are given that when volume $V$ is pumped into reservoir X, it becomes $\frac{3}{8}$ full.

$V=\frac{3}{8}\times C_X$

Rearranging the equation to solve for $C_X$:

$C_X=\frac{8}{3}\times V$

Step 2: Express the total capacity of reservoir Y in terms of $V$.
Similarly, when volume $V$ is pumped into reservoir Y, it becomes $\frac{2}{5}$ full.

$V=\frac{2}{5}\times C_Y$

Rearranging the equation to solve for $C_Y$:

$C_Y=\frac{5}{2}\times V$

Step 3: Calculate what percent the total capacity of reservoir Y is of reservoir X.
To find the percentage of $C_Y$ relative to $C_X$, we use the ratio formula:

$\text{Percentage}=\left(\frac{C_Y}{C_X}\right)\times 100\%$

Substitute the expressions for $C_Y$ and $C_X$ obtained above:

$\text{Percentage}=\left(\frac{\frac{5}{2}V}{\frac{8}{3}V}\right)\times 100\%$

Since $V$ appears in both numerator and denominator, it cancels out:

$\text{Percentage}=\left(\frac{5}{2}\times \frac{3}{8}\right)\times 100\%$

$\text{Percentage}=\frac{15}{16}\times 100\%$

Converting the fraction to a percentage:

$\text{Percentage}=0.9375\times 100\%=93.75\%$

Therefore, the total capacity of reservoir Y is 93.75% of the total capacity of reservoir X.