https://file.aiquickdraw.com/mathbot/file/1726776634026u1d9tt0d.jpg

To solve the equation using Georgia's method:

\[
\frac{13}{3y + 1} = \frac{13}{16}
\]

### Step-by-step solution:

1. **Eliminate the denominators:**  
   Since both sides of the equation have the same numerator (13), we can cross-multiply the denominators directly or cancel out the 13 from both sides:
   
   \[
   3y + 1 = 16
   \]

2. **Solve for \( y \):**
   - Subtract 1 from both sides:
   
     \[
     3y = 16 - 1
     \]
   
     \[
     3y = 15
     \]

   - Divide both sides by 3 to isolate \( y \):
   
     \[
     y = \frac{15}{3} = 5
     \]

Thus, the solution is:

\[
y = 5
\]

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve the equation if the numerators were different?
2. What is the reasoning behind eliminating the same numerator from both sides?
3. How would you solve this equation if the denominator had more complex terms?
4. What if the equation involved fractions on both sides with variables in the numerator?
5. Can you apply a similar technique to solve proportions with different types of operations?

**Tip:** When solving equations with identical numerators, you can often simplify by directly equating the denominators.

Solve the equation \frac{13}{3y + 1} = \frac{13}{16} using Georgia's method.

Learn how to solve the linear equation 13/(3y + 1) = 13/16 using Georgia's method with a step-by-step guide. This problem highlights key algebraic concepts like cross-multiplication and isolating variables. 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