https://file.aiquickdraw.com/mathbot/file/1726998891963qt2pkgom.jpg

The problem is as follows:

\[
\frac{(3x + 5y)}{(3x - 5y)} = \frac{7}{3}
\]

We need to find the ratio \(x : y\).

### Step-by-Step Solution:

1. Start by cross-multiplying to eliminate the fractions:
\[
(3x + 5y) \cdot 3 = (3x - 5y) \cdot 7
\]
\[
9x + 15y = 21x - 35y
\]

2. Bring all terms involving \(x\) and \(y\) to one side:
\[
9x - 21x = -35y - 15y
\]
\[
-12x = -50y
\]

3. Simplify the equation:
\[
x = \frac{50}{12}y
\]
\[
x = \frac{25}{6}y
\]

Thus, the ratio \(x : y = 25 : 6\).

Let me know if you need more details or have any questions!

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Here are five related questions for further exploration:

1. What happens if the equation was \(\frac{(3x + 5y)}{(3x - 5y)} = \frac{3}{7}\)?
2. Can you express \(x\) in terms of \(y\) for any other ratios like \(\frac{5}{3}\)?
3. How would the solution change if the equation involved complex numbers?
4. What if the constants in front of \(x\) and \(y\) were different in the original equation?
5. Could you find a general form for the solution if the ratio was not \(7:3\) but any arbitrary ratio?

### Tip:
Always remember to check for possible simplifications early in the process when solving ratios or proportions.

If (3x + 5y) : (3x - 5y) = 7 : 3, find x : y.

Learn how to solve the equation (3x + 5y) : (3x - 5y) = 7 : 3 and find the ratio of x : y with a detailed step-by-step solution. This problem involves key algebraic concepts like proportions and linear equation manipulation. Suitable for students in Grades 8-10.

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