https://file.aiquickdraw.com/mathbot/file/1729087595941vxqm96nk.jpg

The image shows a sequence of fractions that starts with:

\[
\frac{2}{7} = \frac{4}{x} = \frac{y}{24} = \ldots
\]

To solve this, we aim to find the values of \( x \) and \( y \) that maintain the equality across all the fractions.

1. Starting with \( \frac{2}{7} = \frac{4}{x} \), we can cross-multiply:
\[
2x = 4 \times 7 \quad \Rightarrow \quad 2x = 28 \quad \Rightarrow \quad x = \frac{28}{2} = 14
\]

So, \( x = 14 \).

2. Now, consider \( \frac{4}{14} = \frac{y}{24} \). Again, cross-multiply:
\[
4 \times 24 = 14 \times y \quad \Rightarrow \quad 96 = 14y \quad \Rightarrow \quad y = \frac{96}{14} = \frac{48}{7}
\]

So, \( y = \frac{48}{7} \).

Therefore, the completed equation is:

\[
\frac{2}{7} = \frac{4}{14} = \frac{48}{7} = \ldots
\]

Would you like more details or have any questions about the process?

Here are some related questions:
1. What is cross-multiplication and when is it used?
2. Can fractions always be simplified before solving such equations?
3. How would you check if two fractions are equivalent?
4. What is the general form for solving ratios between multiple fractions?
5. How does solving equations with fractions differ from solving equations with whole numbers?

**Tip:** When solving proportional equations, cross-multiplication is a reliable method to simplify and solve for unknown variables.

Solve the fraction equation sequence: 2/7 = 4/x = y/24.

Learn how to solve the fraction equation sequence 2/7 = 4/x = y/24 using cross-multiplication. This step-by-step guide covers key concepts in fractions and proportions, making it suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation