Lesson 50: Unit Price & Rate Problems

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson focuses on calculating unit prices and solving rate problems using ratios and proportions to handle real-life shopping and work scenarios.

Learning Objectives

• Understand unit price and its importance in decision making.
• Calculate rates and compare costs effectively.
• Solve real-world problems using proportional reasoning.

Topics Covered

• Finding unit prices from total cost and quantity
• Solving rate problems (speed, work, price per item)
• Using proportions to compare options

Key Terms

• Unit Price: The cost per single unit of an item.
• Rate: A ratio that compares two quantities of different units (e.g., miles per hour, dollars per pound).
• Proportion: An equation stating that two ratios are equal, often used to solve rate problems.

Lesson Examples

Example 1: Calculating Unit Price

1. A pack of 12 pencils costs $3.60.
2. Unit price = total cost ÷ quantity = 3.60 ÷ 12
3. Unit price = $0.30 per pencil.

Example 2: Solving a Rate Problem

1. A car travels 180 miles in 3 hours.
2. Rate = distance ÷ time = 180 ÷ 3
3. Rate = 60 miles per hour.

Practice Problems

1. A 5-pound bag of rice costs $12. What is the price per pound?
2. A worker paints 45 square meters in 3 hours. What is the rate in square meters per hour?
3. Two stores sell apples: Store A sells 6 for $4, Store B sells 10 for $7. Which is cheaper per apple?
4. A printer prints 120 pages in 8 minutes. How many pages per minute?

Tips & Common Mistakes

• Always divide the total quantity by the total cost for unit price.
• Check that units match before comparing rates.
• Use proportions carefully; set up ratios consistently.

Summary

Unit price and rate problems are solved using ratios and proportional reasoning. Understanding these concepts helps make informed decisions in everyday situations like shopping, work, and travel.

Challenge Problems

1. A 20-ounce juice costs $5.60. What is the cost per ounce? How much for a 32-ounce bottle?
2. A car travels 150 miles in 2.5 hours. What is the speed in miles per hour? If it continues at this rate, how far will it travel in 6 hours?
3. Store A sells 15 candy bars for $9, Store B sells 20 for $13. Which is the better deal per candy bar?