To show that \(\frac{x + y}{x - y} = \frac{3}{2}\), we can proceed by setting up a proportion and solving it step by step.

### Step 1: Set up the proportion
We are given:
\[
\frac{x + y}{x - y} = \frac{3}{2}
\]

### Step 2: Cross-multiply
To eliminate the fractions, cross-multiply:
\[
2(x + y) = 3(x - y)
\]

### Step 3: Expand both sides
Now expand both sides of the equation:
\[
2x + 2y = 3x - 3y
\]

### Step 4: Rearrange the equation
Move all terms involving \(x\) to one side and all terms involving \(y\) to the other side:
\[
2x - 3x = -3y - 2y
\]
\[
-x = -5y
\]

### Step 5: Simplify
Divide both sides by \(-1\) to solve for \(x\) in terms of \(y\):
\[
x = 5y
\]

### Conclusion
We have shown that if \(x = 5y\), then the given proportion \(\frac{x + y}{x - y} = \frac{3}{2}\) holds true.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:
1. How do you solve proportions in general?
2. What happens if we reverse the ratio (e.g., \(\frac{x - y}{x + y}\))?
3. Can this method work with ratios other than 3:2?
4. How does cross-multiplication help in solving ratios?
5. What are other real-life applications of ratios?

**Tip**: Cross-multiplication is a powerful technique for simplifying and solving equations involving proportions.

Understand how to prove the proportion x + y : x – y = 3 : 2 with a step-by-step solution. This algebra problem focuses on proportions, cross-multiplication, and solving linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation