annette is surveying people in the city about their interest in a new shopping mall. she found that 180…

annette is surveying people in the city about their interest in a new shopping mall. she found that 180 people, or 37.5% of those surveyed, do not want a new mall. how many people did annette survey? people

annette is surveying people in the city about their interest in a new shopping mall. she found that 180 people, or 37.5% of those surveyed, do not want a new mall. how many people did annette survey? people

Answer

Explanation:

Step1: Determine the percentage of people who want a new mall

If (37.5%) do not want a new mall, then the percentage of people who want a new mall is (100% - 37.5%=62.5%)

Step2: Set up an equation to find the total number of people surveyed

Let (x) be the total number of people surveyed. We know that (62.5%) of (x) is (180). Since (62.5%=\frac{62.5}{100}=\frac{5}{8}), the equation is (\frac{5}{8}x = 180)

Step3: Solve for (x)

Multiply both sides of the equation (\frac{5}{8}x=180) by (\frac{8}{5}). So (x = 180\times\frac{8}{5}) [ \begin{align*} x&=\frac{180\times8}{5}\ &=\frac{1440}{5}\ & = 288 \end{align*} ]

Answer:

(288)