Solving scale factor word problems involves understanding the relationship between two proportional quantities. Here are the steps to help you tackle these problems effectively:

**Understand the Problem**: Carefully read the problem to determine what quantities are being compared and what information is provided.**Identify the Scale Factor**: The scale factor is the ratio between the scaled quantity and the original quantity. It can be greater than 1 (enlargement) or less than 1 (reduction).**Set Up a Proportion**: Use the scale factor to set up a proportion. This involves creating a ratio that compares the scaled quantity to the original quantity.**Solve for the Unknown**: Cross-multiply and solve the equation to find the unknown value.**Check Your Work**: Verify your answer by substituting it back into the original proportion to ensure it makes sense.

### Example Problem and Solution

**Problem**:

A map has a scale of 1 inch representing 5 miles. If the distance between two cities on the map is 3 inches, what is the actual distance between the cities?

**Step-by-Step Solution**:

**Understand the Problem**:

- Scale: 1 inch on the map = 5 miles in reality.
- Map distance: 3 inches.
- Find the actual distance.

**Identify the Scale Factor**:

- Scale factor = 1 inch : 5 miles.

**Set Up a Proportion**:

- (Map distance) / (Actual distance) = (Scale map distance) / (Scale real distance).
- 3 inches / x miles = 1 inch / 5 miles.

**Solve for the Unknown**:

- Cross-multiply: 3 inches * 5 miles = 1 inch * x miles.
- 15 miles = x miles.

**Check Your Work**:

- The map distance (3 inches) times the scale factor (5 miles per inch) gives the actual distance: 3 * 5 = 15 miles.

**Answer**: The actual distance between the cities is 15 miles.

### Tips for Solving Scale Factor Problems

**Double-Check Units**: Ensure you’re consistent with units throughout the problem.**Simplify Ratios**: Reduce ratios to their simplest form for easier calculations.**Visual Aids**: Drawing a diagram or using a visual representation can help understand the problem better.**Practice**: The more problems you solve, the more comfortable you’ll become with the process.

By following these steps and practicing regularly, you’ll become proficient in solving scale factor word problems.