Question

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?

Explanation:

Step1: Set up the proportion

Let the total number of people surveyed be \(x\). We know that \(37.5\%=\frac{37.5}{100}\), and the number of people who do not want a new mall is \(180\). So the proportion is \(\frac{37.5}{100}=\frac{180}{x}\).

Step2: Cross - multiply

Cross - multiplying gives \(37.5x = 180\times100\).

Step3: Solve for \(x\)

First, calculate \(180\times100 = 18000\). Then \(x=\frac{18000}{37.5}\).
Since \(18000\div37.5=\frac{18000\times10}{37.5\times10}=\frac{180000}{375}\), and \(180000\div375 = 480\).

Answer:

\(480\)