How to do scale factor word problems?

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

  1. Understand the Problem: Carefully read the problem to determine what quantities are being compared and what information is provided.
  2. 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).
  3. 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.
  4. Solve for the Unknown: Cross-multiply and solve the equation to find the unknown value.
  5. Check Your Work: Verify your answer by substituting it back into the original proportion to ensure it makes sense.

Example Problem and Solution

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:

  1. Understand the Problem:
  • Scale: 1 inch on the map = 5 miles in reality.
  • Map distance: 3 inches.
  • Find the actual distance.
  1. Identify the Scale Factor:
  • Scale factor = 1 inch : 5 miles.
  1. Set Up a Proportion:
  • (Map distance) / (Actual distance) = (Scale map distance) / (Scale real distance).
  • 3 inches / x miles = 1 inch / 5 miles.
  1. Solve for the Unknown:
  • Cross-multiply: 3 inches * 5 miles = 1 inch * x miles.
  • 15 miles = x miles.
  1. 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.

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