video explanation

text explanation

to solve this problem, we need to convert some language into various math operations. first of all, both the percent symbol (%) and the word "percent" mean "to divide by 100". additionally, the word "of" just means "to multiply".

using this information, let's simplify the expression given to us in the prompt:

$3.6\%\text{ of } \dfrac{5\text{x}}{12} =$

$\dfrac{3.6}{100} \times \dfrac{5\text{x}}{12}$

let's get rid of that decimal in the fraction by multiplying both the numerator and denominator by 1, in the form of $\dfrac{10}{10}$:

$\dfrac{3.6}{100} \times \dfrac{10}{10} \times \dfrac{5\text{x}}{12} =$

$\dfrac{36}{1000} \times \dfrac{5\text{x}}{12} =$

$\dfrac{36 \times 5\text{x}}{12 \times 1000}$

we can further simplify this by canceling the common factors in the numerator and denominator:

$\dfrac{12 \times 3 \times 5 \times \text{x}}{12 \times 5 \times 200} =$

$\dfrac{3\text{x}}{200}$

now we have a simplified expression that we need to compare the answer choices to. once again, we'll need to convert from language to math and then simplify the expressions.

a.  3 percent of 20x

$\dfrac{3}{100} \times 20\text{x} =$

$\dfrac{3 \times 20\text{x}}{100} =$

$\dfrac{3 \times 20 \times \text{x}}{20 \times 5} =$

$\dfrac{3\text{x}}{5}$

b.  x percent of $\dfrac{3}{2}$

$\dfrac{\text{x}}{100} \times \dfrac{3}{2} =$

$\dfrac{3\text{x}}{200}$

c.  3x percent of 0.2

$\dfrac{3\text{x}}{100} \times 0.2 =$

$\dfrac{3\text{x}}{100} \times \dfrac{2}{10} =$

$\dfrac{3\text{x} \times 2}{100 \times 10} =$

$\dfrac{3 \times \text{x} \times 2}{100 \times 2 \times 5} =$

$\dfrac{3\text{x}}{500}$

d.  0.05 percent of 3x

$\dfrac{0.05}{100} \times 3\text{x} =$

$\dfrac{\dfrac{5}{100}}{100} \times 3\text{x} =$

$\dfrac{5}{100 \times 100} \times 3\text{x} =$

$\dfrac{5 \times 3\text{x}}{5 \times 20 \times 100} =$

$\dfrac{3\text{x}}{2000}$

e. $\dfrac{3\text{x}}{200}$

thus, the only two statements that are equivalent to the given $\dfrac{3\text{x}}{200}$ are answer choices b and e.