Question

1. on a map, 1/4 inch represent 12 miles. the distance between two cities on that map is 3 1/4 inches. what is the actual distance, in miles, between the two cities? (hint: 1/4 means 0.25)

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(3\frac{1}{4}\) to an improper fraction. \(3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}\)

Step2: Set up proportion

We know that \(\frac{1}{4}\) inch (or \(0.25\) inch) represents \(12\) miles. Let \(x\) be the actual distance. We set up the proportion \(\frac{0.25}{12}=\frac{\frac{13}{4}}{x}\)

Step3: Cross - multiply

Cross - multiply gives us \(0.25x=12\times\frac{13}{4}\)

Step4: Simplify the right - hand side

\(12\times\frac{13}{4}=\frac{12\times13}{4}=3\times13 = 39\)

Step5: Solve for \(x\)

Since \(0.25x = 39\), and \(0.25=\frac{1}{4}\), then \(x=39\div0.25=39\times4 = 156\)

Answer:

\(156\) miles