# 55 Lesson 6 Solving Problems By Finding Equivalent Ratios Answer Key

## Lesson 6: Solving Problems by Finding Equivalent Ratios Answer Key

### Introduction

Mathematics can often seem like a daunting subject, especially when it comes to solving problems. However, with the right tools and strategies, anyone can become proficient in solving mathematical problems. In this article, we will be exploring the answer key for Lesson 6: Solving Problems by Finding Equivalent Ratios. By understanding the concepts and techniques presented in this lesson, you will be well-equipped to tackle a wide range of mathematical problems that involve ratios.

### Understanding Equivalent Ratios

Before we dive into the answer key for Lesson 6, let's take a moment to review the concept of equivalent ratios. Equivalent ratios are ratios that have the same value. In other words, they represent the same relationship between two quantities, but may be expressed in different forms. To determine if two ratios are equivalent, we can cross-multiply and check if the products are equal. If they are, then the ratios are equivalent.

### Problem 1: Finding Equivalent Ratios

In this problem, we are given a ratio and tasked with finding additional ratios that are equivalent to the given ratio. Let's take a look at the problem:

Problem: The ratio of red to blue marbles in a bag is 3:5. Find two additional ratios that are equivalent to this ratio.

Solution: To find two additional ratios that are equivalent to the given ratio, we can multiply both the numerator and denominator of the ratio by the same number. Let's multiply by 2:

Original ratio: 3:5

Equivalent ratio 1: 6:10

Equivalent ratio 2: 9:15

By multiplying both the numerator and denominator of the original ratio by 2, we obtain two additional ratios that are equivalent to the given ratio.

### Problem 2: Solving Word Problems Using Equivalent Ratios

In this problem, we are presented with a word problem that involves equivalent ratios. Let's take a look at the problem:

Problem: A recipe calls for 2 cups of flour and 3 cups of water. If you want to make half a batch of the recipe, how much flour and water do you need?

Solution: To solve this problem, we can use the concept of equivalent ratios. Since we want to make half a batch of the recipe, we need to find the equivalent ratio for half of the given amounts of flour and water. Let's set up the ratios:

Original ratio: 2 cups of flour to 3 cups of water

Equivalent ratio: x cups of flour to y cups of water

To find the values of x and y, we can set up a proportion:

(2 cups of flour / 3 cups of water) = (x cups of flour / y cups of water)

Cross-multiplying, we get:

2y = 3x

Since we want to make half a batch, we can let x = 1 and solve for y:

2y = 3(1)

y = 3/2

Therefore, we need 1 cup of flour and 3/2 cups (or 1.5 cups) of water to make half a batch of the recipe.

### Problem 3: Applying Equivalent Ratios to Real-Life Scenarios

In this problem, we will be applying the concept of equivalent ratios to a real-life scenario. Let's take a look at the problem:

Problem: A map scale indicates that 1 inch on the map represents 10 miles in real life. If the distance between two cities on the map is 5 inches, what is the actual distance between the cities?

Solution: To solve this problem, we can set up a proportion using the given information:

(1 inch on the map / 10 miles in real life) = (5 inches on the map / x miles in real life)

Cross-multiplying, we get:

1 * x = 10 * 5

x = 50

Therefore, the actual distance between the cities is 50 miles.

### Conclusion

By understanding and applying the concepts of equivalent ratios, you can become proficient in solving a wide range of mathematical problems. In this article, we explored the answer key for Lesson 6: Solving Problems by Finding Equivalent Ratios. We tackled problems involving finding equivalent ratios, solving word problems using equivalent ratios, and applying equivalent ratios to real-life scenarios. With practice and perseverance, you can master the art of solving mathematical problems using equivalent ratios.