https://file.aiquickdraw.com/mathbot/file/1725396209042xraukxkg.jpg

The problem shown in the image states:

"Alex is younger than Theresa by 9 years. If their ages are in the respective ratio of 7:9, how old is Alex?"

Let's break this down and solve the problem step by step.

### Step 1: Define Variables
Let:
- Alex's age be \( A \)
- Theresa's age be \( T \)

### Step 2: Set Up Equations Based on the Problem Statement
1. **Age difference**:  
   \( T = A + 9 \) (since Alex is 9 years younger than Theresa).

2. **Age ratio**:  
   The ratio of their ages is given as 7:9, which means:
   \[
   \frac{A}{T} = \frac{7}{9}
   \]
   This can be rewritten as:
   \[
   9A = 7T
   \]

### Step 3: Substitute and Solve the Equations
Substitute \( T = A + 9 \) into the ratio equation \( 9A = 7T \):
\[
9A = 7(A + 9)
\]
Expand and solve for \( A \):
\[
9A = 7A + 63
\]
\[
9A - 7A = 63
\]
\[
2A = 63
\]
\[
A = \frac{63}{2}
\]
\[
A = 31.5
\]

### Conclusion
Alex is 31.5 years old.

Would you like more details on this solution, or do you have any questions? Here are some related questions to expand your understanding:

1. If Alex is 31.5 years old, how old is Theresa?
2. What would be Alex's age if the ratio of their ages was 3:4?
3. How would the solution change if Alex were older than Theresa by 9 years instead?
4. What is the importance of ratios in solving age-related problems?
5. Can this problem be solved using a different method, such as using a system of linear equations?

**Tip**: When solving word problems, always begin by defining variables and translating the words into mathematical equations. This approach makes it easier to solve the problem systematically.

Alex is younger than Theresa by 9 years. If their ages are in the respective ratio of 7:9, how old is Alex?

Learn how to solve an age-related problem where Alex is 9 years younger than Theresa, and their ages are in the ratio of 7:9. This solution covers key algebraic concepts, including setting up and solving linear equations. Suitable for students in Grades 6-8.

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