Question

solve for the base in the following.
$31\frac{1}{4}\\%$ of \\_\\_\\_\\_\\_ people is 120 people.

$31\frac{1}{4}\\%$ of $\square$ people is 120 people.
(simplify your answer.)

Explanation:

Step1: Convert the mixed fraction percentage to a decimal

First, we convert \( 31\frac{1}{4}\% \) to a decimal. \( 31\frac{1}{4} = 31.25 \), so \( 31\frac{1}{4}\% = 0.3125 \).

Step2: Set up the equation

Let the base (the number we are looking for) be \( x \). The problem states that \( 31\frac{1}{4}\% \) of \( x \) is 120, so we can write the equation as \( 0.3125x = 120 \).

Step3: Solve for \( x \)

To solve for \( x \), we divide both sides of the equation by 0.3125: \( x=\frac{120}{0.3125} \). Calculating this, we get \( x = 384 \).

Answer:

384