https://file.aiquickdraw.com/mathbot/file/172874638407359rajgqu.jpg

Let's analyze the problem step by step:

1. **Given Information:**
   - Mr. Anderson is **10 times older** than his daughter currently.
   - In **32 years**, the **ratio** of their ages will be **2:1**.

2. **Unknown Variables:**
   Let:
   - Mr. Anderson's current age be \( M \).
   - His daughter's current age be \( D \).

3. **Formulation of Equations:**

   From the first statement:
   \[
   M = 10D \tag{1}
   \]

   From the second statement (in 32 years, their ages will have a ratio of 2:1):
   \[
   \frac{M + 32}{D + 32} = 2 \tag{2}
   \]

4. **Solve the system of equations:**

   - Substitute \( M = 10D \) from equation (1) into equation (2):
     \[
     \frac{10D + 32}{D + 32} = 2
     \]

   - Multiply both sides by \( D + 32 \):
     \[
     10D + 32 = 2(D + 32)
     \]

   - Expand the right-hand side:
     \[
     10D + 32 = 2D + 64
     \]

   - Simplify and solve for \( D \):
     \[
     10D - 2D = 64 - 32
     \]
     \[
     8D = 32
     \]
     \[
     D = 4
     \]

   Therefore, Mr. Anderson's daughter is currently **4 years old**.

5. **Find Mr. Anderson's current age:**

   Using equation (1), where \( M = 10D \):
   \[
   M = 10 \times 4 = 40
   \]

   So, Mr. Anderson is currently **40 years old**.

---

Would you like further details or have any questions?

Here are 5 related questions:
1. What will the ages of Mr. Anderson and his daughter be in 32 years?
2. How would the solution change if Mr. Anderson were 5 times older instead of 10?
3. How can you verify that the ratio will indeed be 2:1 in 32 years?
4. What are some real-world applications of solving age-related ratio problems?
5. If another person were involved in the problem, how would you modify the system of equations?

**Tip:** When solving ratio problems, always set up clear relationships using variables and translate word problems into equations step by step!

Mr. Anderson is 10 times older than his daughter. In 32 years, the ratio of their ages will be 2:1. How old is Mr. Anderson now?

Learn how to determine Mr. Anderson's current age using algebraic equations and ratios. This problem explores the relationship between age ratios and linear equations, suitable for students in Grades 6-8.

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