Lesson: Ratio Word Problems

Introduction

Ratios are a way to compare two quantities. In this lesson, we will learn how to solve word problems that involve ratios and proportions.

Key Concepts

• A ratio compares two quantities, written as $a : b$ or $\frac{a}{b}$.
• A proportion states that two ratios are equal, written as $\frac{a}{b} = \frac{c}{d}$.

Example Problem

Problem: If the ratio of cats to dogs in a pet store is 3:4 and there are 12 cats, how many dogs are there?

Steps to Solve:

1. Identify the ratio: The ratio of cats to dogs is $3:4$. This means for every 3 cats, there are 4 dogs.
2. Set up the equation: Let $x$ be the number of dogs. We can set up the proportion: $\frac{3}{4} = \frac{12}{x}$
3. Cross-multiply to solve: $3x = 4 \cdot 12$ $3x = 48$
4. Solve for $x$: $x = \frac{48}{3} = 16$

Conclusion

There are 16 dogs in the pet store.

Key Questions

• What is a ratio?
• How do you set up a proportion from a word problem?
• What steps do you follow to solve a ratio word problem?

Practice Problems

1. The ratio of apples to oranges is 5:3. If there are 30 apples, how many oranges are there?
2. In a class, the ratio of boys to girls is 2:3. If there are 10 boys, how many girls are in the class?

Summary

Understanding how to interpret and solve ratio word problems is essential for applying ratios in real-life situations.