Question

$x$ is $40\%$ of $y$. 50% of $y$ is $40$.

Then $16$ is what percent of $x$?

• A. $40$
• B. $60$
• C. $50$
• D. $45$

Answer 1

The correct option is C $50$

50%: You can translate the first two sentences directly into equations:

$x$ is 40% of $y\to x=\left(\frac{40}{100}\right)$

50% of $y$ is 40 $\to \left(\frac{50}{100}\right)y=40$

You can solve the second equation for $y$:

$\left(\frac{50}{100}\right)y=40$

$\left(\frac{1}{2}\right)y=40$

$y=80$

Now you can replace y with 80 in the first equation to solve for $x$:

$x=\left(\frac{40}{100}\right)\left(80\right)$

$x=\frac{4}{10}\times 80$

$x=4\times 8=32$

Be careful now. The question asks, "16 is what percent of $x$?"

You know that x = 32, so this question is really asking, "16 is what percent of 32?"

Create a new variable (z) to represent the unknown value in the question and solve:

$16=\frac{z}{100}\times 32$

$16\times \frac{100}{32}=z$

$1\times \frac{100}{2}=z$

$50=z$

Thus, 16 is 50% of $x$,